---
_id: '14930'
abstract:
- lang: eng
text: In this paper we investigate locally free representations of a quiver Q over
a commutative Frobenius algebra R by arithmetic Fourier transform. When the base
field is finite we prove that the number of isomorphism classes of absolutely
indecomposable locally free representations of fixed rank is independent of the
orientation of Q. We also prove that the number of isomorphism classes of locally
free absolutely indecomposable representations of the preprojective algebra of
Q over R equals the number of isomorphism classes of locally free absolutely indecomposable
representations of Q over R[t]/(t2). Using these results together with results
of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification
of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally
free representations of Q over R is finite. Finally when the representation is
free of rank 1 at each vertex of Q, we study the function that counts the number
of isomorphism classes of absolutely indecomposable locally free representations
of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial
in q and their generating function is rational and satisfies a functional equation.
acknowledgement: Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer
for explaining their work but also for sharing some unpublished results with us.
We also thank the referee for many useful suggestions. We would like to thank Tommaso
Scognamiglio for pointing out a mistake in the proof of Proposition 5.17 in an earlier
version of the paper. We would like also to thank Alexander Beilinson, Bill Crawley-Boevey,
Joel Kamnitzer, and Peng Shan for useful discussions.
article_number: '20'
article_processing_charge: No
article_type: original
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Emmanuel
full_name: Letellier, Emmanuel
last_name: Letellier
- first_name: Fernando
full_name: Rodriguez-Villegas, Fernando
last_name: Rodriguez-Villegas
citation:
ama: Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of
quivers over commutative Frobenius algebras. Selecta Mathematica. 2024;30(2).
doi:10.1007/s00029-023-00914-2
apa: Hausel, T., Letellier, E., & Rodriguez-Villegas, F. (2024). Locally free
representations of quivers over commutative Frobenius algebras. Selecta Mathematica.
Springer Nature. https://doi.org/10.1007/s00029-023-00914-2
chicago: Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally
Free Representations of Quivers over Commutative Frobenius Algebras.” Selecta
Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00914-2.
ieee: T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations
of quivers over commutative Frobenius algebras,” Selecta Mathematica, vol.
30, no. 2. Springer Nature, 2024.
ista: Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations
of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20.
mla: Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative
Frobenius Algebras.” Selecta Mathematica, vol. 30, no. 2, 20, Springer
Nature, 2024, doi:10.1007/s00029-023-00914-2.
short: T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024).
date_created: 2024-02-04T23:00:53Z
date_published: 2024-01-27T00:00:00Z
date_updated: 2024-02-05T12:58:21Z
day: '27'
department:
- _id: TaHa
doi: 10.1007/s00029-023-00914-2
intvolume: ' 30'
issue: '2'
language:
- iso: eng
month: '01'
oa_version: None
publication: Selecta Mathematica
publication_identifier:
eissn:
- 1420-9020
issn:
- 1022-1824
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Locally free representations of quivers over commutative Frobenius algebras
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2024'
...
---
_id: '14986'
abstract:
- lang: eng
text: We prove a version of the tamely ramified geometric Langlands correspondence
in positive characteristic for GLn(k). Let k be an algebraically closed field
of characteristic p>n. Let X be a smooth projective curve over k with marked points,
and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P
the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli
stack of parabolic flat connections such that the residue is nilpotent with respect
to the parabolic reduction at each marked point. We construct an equivalence between
the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an
open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod)
of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of
crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman
to the tamely ramified case. We also prove a correspondence between flat connections
on X with regular singularities and meromorphic Higgs bundles on the Frobenius
twist X(1) of X with first order poles .
acknowledgement: "This work was supported by the NSF [DMS-1502125to S.S.]; and the
European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
grant agreement [101034413 to S.S.].\r\nI would like to thank my advisor Tom Nevins
for many helpful discussions on this subject and for his comments on this paper.
I would like to thank Christopher Dodd, Michael Groechenig, and Tamas Hausel for
helpful conversations. I would like to thank Tsao-Hsien Chen for useful comments
on an earlier version of this paper."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Shiyu
full_name: Shen, Shiyu
id: 544cccd3-9005-11ec-87bc-94aef1c5b814
last_name: Shen
citation:
ama: Shen S. Tamely ramified geometric Langlands correspondence in positive characteristic.
International Mathematics Research Notices. 2024. doi:10.1093/imrn/rnae005
apa: Shen, S. (2024). Tamely ramified geometric Langlands correspondence in positive
characteristic. International Mathematics Research Notices. Oxford University
Press. https://doi.org/10.1093/imrn/rnae005
chicago: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
Characteristic.” International Mathematics Research Notices. Oxford University
Press, 2024. https://doi.org/10.1093/imrn/rnae005.
ieee: S. Shen, “Tamely ramified geometric Langlands correspondence in positive characteristic,”
International Mathematics Research Notices. Oxford University Press, 2024.
ista: Shen S. 2024. Tamely ramified geometric Langlands correspondence in positive
characteristic. International Mathematics Research Notices.
mla: Shen, Shiyu. “Tamely Ramified Geometric Langlands Correspondence in Positive
Characteristic.” International Mathematics Research Notices, Oxford University
Press, 2024, doi:10.1093/imrn/rnae005.
short: S. Shen, International Mathematics Research Notices (2024).
date_created: 2024-02-14T12:16:17Z
date_published: 2024-02-05T00:00:00Z
date_updated: 2024-02-19T10:22:44Z
day: '05'
department:
- _id: TaHa
doi: 10.1093/imrn/rnae005
ec_funded: 1
external_id:
arxiv:
- '1810.12491'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1093/imrn/rnae005
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: epub_ahead
publisher: Oxford University Press
quality_controlled: '1'
status: public
title: Tamely ramified geometric Langlands correspondence in positive characteristic
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '12329'
abstract:
- lang: eng
text: In this article, we develop two independent and new approaches to model epidemic
spread in a network. Contrary to the most studied models, those developed here
allow for contacts with different probabilities of transmitting the disease (transmissibilities).
We then examine each of these models using some mean field type approximations.
The first model looks at the late-stage effects of an epidemic outbreak and allows
for the computation of the probability that a given vertex was infected. This
computation is based on a mean field approximation and only depends on the number
of contacts and their transmissibilities. This approach shares many similarities
with percolation models in networks. The second model we develop is a dynamic
model which we analyze using a mean field approximation which highly reduces the
dimensionality of the system. In particular, the original system which individually
analyses each vertex of the network is reduced to one with as many equations as
different transmissibilities. Perhaps the greatest contribution of this article
is the observation that, in both these models, the existence and size of an epidemic
outbreak are linked to the properties of a matrix which we call the R-matrix.
This is a generalization of the basic reproduction number which more precisely
characterizes the main routes of infection.
acknowledgement: Gonçalo Oliveira is supported by the NOMIS Foundation, Fundação Serrapilheira
1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and by FAPERJ through
the grant Jovem Cientista do Nosso Estado E-26/202.793/2019.
article_number: '468'
article_processing_charge: No
article_type: original
author:
- first_name: Arturo
full_name: Gómez, Arturo
last_name: Gómez
- first_name: Goncalo
full_name: Oliveira, Goncalo
id: 58abbde8-f455-11eb-a497-98c8fd71b905
last_name: Oliveira
citation:
ama: Gómez A, Oliveira G. New approaches to epidemic modeling on networks. Scientific
Reports. 2023;13. doi:10.1038/s41598-022-19827-9
apa: Gómez, A., & Oliveira, G. (2023). New approaches to epidemic modeling on
networks. Scientific Reports. Springer Nature. https://doi.org/10.1038/s41598-022-19827-9
chicago: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling
on Networks.” Scientific Reports. Springer Nature, 2023. https://doi.org/10.1038/s41598-022-19827-9.
ieee: A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,”
Scientific Reports, vol. 13. Springer Nature, 2023.
ista: Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks.
Scientific Reports. 13, 468.
mla: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on
Networks.” Scientific Reports, vol. 13, 468, Springer Nature, 2023, doi:10.1038/s41598-022-19827-9.
short: A. Gómez, G. Oliveira, Scientific Reports 13 (2023).
date_created: 2023-01-22T23:00:55Z
date_published: 2023-01-10T00:00:00Z
date_updated: 2023-08-01T12:31:40Z
day: '10'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1038/s41598-022-19827-9
external_id:
isi:
- '001003345000051'
file:
- access_level: open_access
checksum: a8b83739f4a951e83e0b2a778f03b327
content_type: application/pdf
creator: dernst
date_created: 2023-01-23T07:53:23Z
date_updated: 2023-01-23T07:53:23Z
file_id: '12336'
file_name: 2023_ScientificReports_Gomez.pdf
file_size: 2167792
relation: main_file
success: 1
file_date_updated: 2023-01-23T07:53:23Z
has_accepted_license: '1'
intvolume: ' 13'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Scientific Reports
publication_identifier:
eissn:
- 2045-2322
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New approaches to epidemic modeling on networks
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 13
year: '2023'
...
---
_id: '13966'
abstract:
- lang: eng
text: We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation
energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams,
we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation
energies up to n=5, with quadratic scaling in the number of basis functions. Our
technique reduces the computational complexity of the molecular many-fermion correlation
problem, opening up the possibility of low-scaling, accurate stochastic computations
for a wide class of many-body systems described by Hugenholtz diagrams.
acknowledgement: We acknowledge stimulating discussions with Sergey Varganov, Artur
Izmaylov, Jacek Kłos, Piotr Żuchowski, Dominika Zgid, Nikolay Prokof'ev, Boris Svistunov,
Robert Parrish, and Andreas Heßelmann. G.B. and Q.P.H. acknowledge support from
the Austrian Science Fund (FWF) under Projects No. M2641-N27 and No. M2751. M.L.
acknowledges support by the FWF under Project No. P29902-N27, and by the European
Research Council (ERC) Starting Grant No. 801770 (ANGULON). T.V.T. was supported
by the NSF CAREER award No. PHY-2045681. This work is supported by the German Research
Foundation (DFG) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg
STRUCTURES Excellence Cluster). The authors acknowledge support by the state of
Baden-Württemberg through bwHPC.
article_number: '045115'
article_processing_charge: No
article_type: original
author:
- first_name: Giacomo
full_name: Bighin, Giacomo
id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87
last_name: Bighin
orcid: 0000-0001-8823-9777
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: T. V.
full_name: Tscherbul, T. V.
last_name: Tscherbul
citation:
ama: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. Diagrammatic Monte Carlo for electronic
correlation in molecules: High-order many-body perturbation theory with low scaling.
Physical Review B. 2023;108(4). doi:10.1103/PhysRevB.108.045115'
apa: 'Bighin, G., Ho, Q. P., Lemeshko, M., & Tscherbul, T. V. (2023). Diagrammatic
Monte Carlo for electronic correlation in molecules: High-order many-body perturbation
theory with low scaling. Physical Review B. American Physical Society.
https://doi.org/10.1103/PhysRevB.108.045115'
chicago: 'Bighin, Giacomo, Quoc P Ho, Mikhail Lemeshko, and T. V. Tscherbul. “Diagrammatic
Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation
Theory with Low Scaling.” Physical Review B. American Physical Society,
2023. https://doi.org/10.1103/PhysRevB.108.045115.'
ieee: 'G. Bighin, Q. P. Ho, M. Lemeshko, and T. V. Tscherbul, “Diagrammatic Monte
Carlo for electronic correlation in molecules: High-order many-body perturbation
theory with low scaling,” Physical Review B, vol. 108, no. 4. American
Physical Society, 2023.'
ista: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. 2023. Diagrammatic Monte Carlo
for electronic correlation in molecules: High-order many-body perturbation theory
with low scaling. Physical Review B. 108(4), 045115.'
mla: 'Bighin, Giacomo, et al. “Diagrammatic Monte Carlo for Electronic Correlation
in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical
Review B, vol. 108, no. 4, 045115, American Physical Society, 2023, doi:10.1103/PhysRevB.108.045115.'
short: G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023).
date_created: 2023-08-06T22:01:10Z
date_published: 2023-07-15T00:00:00Z
date_updated: 2023-08-07T08:41:29Z
day: '15'
department:
- _id: MiLe
- _id: TaHa
doi: 10.1103/PhysRevB.108.045115
ec_funded: 1
external_id:
arxiv:
- '2203.12666'
intvolume: ' 108'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.12666
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 26986C82-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02641
name: A path-integral approach to composite impurities
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
- _id: 26031614-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P29902
name: Quantum rotations in the presence of a many-body environment
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Diagrammatic Monte Carlo for electronic correlation in molecules: High-order
many-body perturbation theory with low scaling'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 108
year: '2023'
...
---
_id: '14239'
abstract:
- lang: eng
text: "Given a resolution of rational singularities π:X~→X over a field of characteristic
zero, we use a Hodge-theoretic argument to prove that the image of the functor
\ Rπ∗:Db(X~)→Db(X)\r\n between bounded derived categories of coherent sheaves
generates Db(X)\r\n as a triangulated category. This gives a weak version of
the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21].
The same result is established more generally for proper (not necessarily birational)
morphisms π:X~→X , with X~\r\n smooth, satisfying Rπ∗(OX~)=OX ."
acknowledgement: "We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara,
Sándor Kovács, Alexander Kuznetsov, Mircea Musta ă, Nebojsa Pavic, Pavel Sechin,
and Michael Wemyss for discussions and e-mail correspondence. We also thank the
anonymous referee for the helpful comments. M.M. was supported by the Institute
of Science and Technology Austria. This project has received funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement no. 101034413. E.S. was partially supported by the EPSRC grant EP/T019379/1
“Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy
grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler
Varieties.”\r\n\r\n"
article_number: e66
article_processing_charge: Yes
article_type: original
author:
- first_name: Mirko
full_name: Mauri, Mirko
id: 2cf70c34-09c1-11ed-bd8d-c34fac206130
last_name: Mauri
- first_name: Evgeny
full_name: Shinder, Evgeny
last_name: Shinder
citation:
ama: Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational
singularities. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.65
apa: Mauri, M., & Shinder, E. (2023). Homological Bondal-Orlov localization
conjecture for rational singularities. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2023.65
chicago: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization
Conjecture for Rational Singularities.” Forum of Mathematics, Sigma. Cambridge
University Press, 2023. https://doi.org/10.1017/fms.2023.65.
ieee: M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture
for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge
University Press, 2023.
ista: Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture
for rational singularities. Forum of Mathematics, Sigma. 11, e66.
mla: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture
for Rational Singularities.” Forum of Mathematics, Sigma, vol. 11, e66,
Cambridge University Press, 2023, doi:10.1017/fms.2023.65.
short: M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).
date_created: 2023-08-27T22:01:16Z
date_published: 2023-08-03T00:00:00Z
date_updated: 2023-12-13T12:18:18Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1017/fms.2023.65
ec_funded: 1
external_id:
arxiv:
- '2212.06786'
isi:
- '001041926700001'
file:
- access_level: open_access
checksum: c36241750cc5cb06890aec0ecdfee626
content_type: application/pdf
creator: dernst
date_created: 2023-09-05T06:43:11Z
date_updated: 2023-09-05T06:43:11Z
file_id: '14266'
file_name: 2023_ForumMathematics_Mauri.pdf
file_size: 280865
relation: main_file
success: 1
file_date_updated: 2023-09-05T06:43:11Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homological Bondal-Orlov localization conjecture for rational singularities
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '13268'
abstract:
- lang: eng
text: We give a simple argument to prove Nagai’s conjecture for type II degenerations
of compact hyperkähler manifolds and cohomology classes of middle degree. Under
an additional assumption, the techniques yield the conjecture in arbitrary degree.
This would complete the proof of Nagai’s conjecture in general, as it was proved
already for type I degenerations by Kollár, Laza, Saccà, and Voisin [10] and independently
by Soldatenkov [18], while it is immediate for type III degenerations. Our arguments
are close in spirit to a recent paper by Harder [8] proving similar results for
the restrictive class of good degenerations.
acknowledgement: The first author is supported by the ERC Synergy Grant HyperK. The
second author is supported by the Max Planck Institute for Mathematics and the Institute
of Science and Technology Austria. This project has received funding from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
grant agreement No 101034413.
article_processing_charge: No
article_type: original
author:
- first_name: D.
full_name: Huybrechts, D.
last_name: Huybrechts
- first_name: Mirko
full_name: Mauri, Mirko
id: 2cf70c34-09c1-11ed-bd8d-c34fac206130
last_name: Mauri
citation:
ama: Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. Mathematical
Research Letters. 2023;30(1):125-141. doi:10.4310/mrl.2023.v30.n1.a6
apa: Huybrechts, D., & Mauri, M. (2023). On type II degenerations of hyperkähler
manifolds. Mathematical Research Letters. International Press. https://doi.org/10.4310/mrl.2023.v30.n1.a6
chicago: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler
Manifolds.” Mathematical Research Letters. International Press, 2023. https://doi.org/10.4310/mrl.2023.v30.n1.a6.
ieee: D. Huybrechts and M. Mauri, “On type II degenerations of hyperkähler manifolds,”
Mathematical Research Letters, vol. 30, no. 1. International Press, pp.
125–141, 2023.
ista: Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds.
Mathematical Research Letters. 30(1), 125–141.
mla: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.”
Mathematical Research Letters, vol. 30, no. 1, International Press, 2023,
pp. 125–41, doi:10.4310/mrl.2023.v30.n1.a6.
short: D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 125–141.
date_created: 2023-07-23T22:01:14Z
date_published: 2023-06-21T00:00:00Z
date_updated: 2024-01-16T12:00:47Z
day: '21'
department:
- _id: TaHa
doi: 10.4310/mrl.2023.v30.n1.a6
ec_funded: 1
external_id:
arxiv:
- '2108.01587'
isi:
- '001027656000006'
intvolume: ' 30'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2108.01587
month: '06'
oa: 1
oa_version: Preprint
page: 125-141
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematical Research Letters
publication_identifier:
eissn:
- 1945-001X
issn:
- 1073-2780
publication_status: published
publisher: International Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On type II degenerations of hyperkähler manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...
---
_id: '14244'
abstract:
- lang: eng
text: "In this paper, we determine the motivic class — in particular, the weight
polynomial and conjecturally the Poincaré polynomial — of the open de Rham space,
defined and studied by Boalch, of certain moduli spaces of irregular meromorphic
connections on the trivial rank \r\n bundle on P1. The computation is by motivic
Fourier transform. We show that the result satisfies the purity conjecture, that
is, it agrees with the pure part of the conjectured mixed Hodge polynomial of
the corresponding wild character variety. We also identify the open de Rham spaces
with quiver varieties with multiplicities of Yamakawa and Geiss–Leclerc–Schröer.
We finish with constructing natural complete hyperkähler metrics on them, which
in the four-dimensional cases are expected to be of type ALF."
acknowledgement: We would like to thank Gergely Bérczy, Roger Bielawski, Philip Boalch,
Sergey Cherkis, Andrew Dancer, Brent Doran, Eloïse Hamilton, Frances Kirwan, Bernard
Leclerc, Emmanuel Letellier, Alessia Mandini, Maxence Mayrand, András Némethi, Szilárd
Szabó, and Daisuke Yamakawa for discussions related to the paper. We especially
thank the referee for an extensive list of very careful comments. At various stages
of this project, the authors were supported by the Advanced Grant “Arithmetic and
physics of Higgs moduli spaces” no. 320593 of the European Research Council, by
grant no. 153627 and NCCR SwissMAP, both funded by the Swiss National Science Foundation
as well as by EPF Lausanne and IST Austria. In the final stages of this project,
MLW was supported by SFB/TR 45 “Periods, moduli and arithmetic of algebraic varieties,”
subproject M08-10 “Moduli of vector bundles on higher-dimensional varieties.” DW
was also supported by the Fondation Sciences Mathématiques de Paris, as well as
public grants overseen by the Agence national de la recherche (ANR) of France as
part of the Investissements d'avenir program, under reference numbers ANR-10-LABX-0098
and ANR-15-CE40-0008 (Défigéo).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Michael Lennox
full_name: Wong, Michael Lennox
last_name: Wong
- first_name: Dimitri
full_name: Wyss, Dimitri
last_name: Wyss
citation:
ama: Hausel T, Wong ML, Wyss D. Arithmetic and metric aspects of open de Rham spaces.
Proceedings of the London Mathematical Society. 2023;127(4):958-1027. doi:10.1112/plms.12555
apa: Hausel, T., Wong, M. L., & Wyss, D. (2023). Arithmetic and metric aspects
of open de Rham spaces. Proceedings of the London Mathematical Society.
Wiley. https://doi.org/10.1112/plms.12555
chicago: Hausel, Tamás, Michael Lennox Wong, and Dimitri Wyss. “Arithmetic and Metric
Aspects of Open de Rham Spaces.” Proceedings of the London Mathematical Society.
Wiley, 2023. https://doi.org/10.1112/plms.12555.
ieee: T. Hausel, M. L. Wong, and D. Wyss, “Arithmetic and metric aspects of open
de Rham spaces,” Proceedings of the London Mathematical Society, vol. 127,
no. 4. Wiley, pp. 958–1027, 2023.
ista: Hausel T, Wong ML, Wyss D. 2023. Arithmetic and metric aspects of open de
Rham spaces. Proceedings of the London Mathematical Society. 127(4), 958–1027.
mla: Hausel, Tamás, et al. “Arithmetic and Metric Aspects of Open de Rham Spaces.”
Proceedings of the London Mathematical Society, vol. 127, no. 4, Wiley,
2023, pp. 958–1027, doi:10.1112/plms.12555.
short: T. Hausel, M.L. Wong, D. Wyss, Proceedings of the London Mathematical Society
127 (2023) 958–1027.
date_created: 2023-08-27T22:01:18Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:56:10Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/plms.12555
ec_funded: 1
external_id:
arxiv:
- '1807.04057'
isi:
- '001049312700001'
file:
- access_level: open_access
checksum: 2af4d2d6a8ae42f7d3fba0188e79ae82
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:56:00Z
date_updated: 2024-01-30T12:56:00Z
file_id: '14910'
file_name: 2023_ProcLondonMathSoc_Hausel.pdf
file_size: 651335
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:56:00Z
has_accepted_license: '1'
intvolume: ' 127'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 958-1027
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 25E6C798-B435-11E9-9278-68D0E5697425
grant_number: '153627'
name: Arithmetic quantization of character and quiver varities
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and metric aspects of open de Rham spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 127
year: '2023'
...
---
_id: '12303'
abstract:
- lang: eng
text: We construct for each choice of a quiver Q, a cohomology theory A, and a poset
P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple
groups and the loop Grassmannians of based quadratic forms. The addition of a
“dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated
by the program of introducing an inner cohomology theory in algebraic geometry
adequate for the Geometric Langlands program (Mirković, Some extensions of the
notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić
issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups
from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic
quantum groups, preprint. arxiv1708.01418).
acknowledgement: I.M. thanks Zhijie Dong for long-term discussions on the material
that entered this work. We thank Misha Finkelberg for pointing out errors in earlier
versions. His advice and his insistence have led to a much better paper. A part
of the writing was done at the conference at IST (Vienna) attended by all coauthors.
We therefore thank the organizers of the conference and the support of ERC Advanced
Grant Arithmetic and Physics of Higgs moduli spaces No. 320593. The work of I.M.
was partially supported by NSF grants. The work of Y.Y. was partially supported
by the Australian Research Council (ARC) via the award DE190101231. The work of
G.Z. was partially supported by ARC via the award DE190101222.
alternative_title:
- Trends in Mathematics
article_processing_charge: No
author:
- first_name: Ivan
full_name: Mirković, Ivan
last_name: Mirković
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: 'Mirković I, Yang Y, Zhao G. Loop Grassmannians of Quivers and Affine Quantum
Groups. In: Baranovskky V, Guay N, Schedler T, eds. Representation Theory and
Algebraic Geometry. 1st ed. TM. Cham: Springer Nature; Birkhäuser; 2022:347-392.
doi:10.1007/978-3-030-82007-7_8'
apa: 'Mirković, I., Yang, Y., & Zhao, G. (2022). Loop Grassmannians of Quivers
and Affine Quantum Groups. In V. Baranovskky, N. Guay, & T. Schedler (Eds.),
Representation Theory and Algebraic Geometry (1st ed., pp. 347–392). Cham:
Springer Nature; Birkhäuser. https://doi.org/10.1007/978-3-030-82007-7_8'
chicago: 'Mirković, Ivan, Yaping Yang, and Gufang Zhao. “Loop Grassmannians of Quivers
and Affine Quantum Groups.” In Representation Theory and Algebraic Geometry,
edited by Vladimir Baranovskky, Nicolas Guay, and Travis Schedler, 1st ed., 347–92.
TM. Cham: Springer Nature; Birkhäuser, 2022. https://doi.org/10.1007/978-3-030-82007-7_8.'
ieee: 'I. Mirković, Y. Yang, and G. Zhao, “Loop Grassmannians of Quivers and Affine
Quantum Groups,” in Representation Theory and Algebraic Geometry, 1st ed.,
V. Baranovskky, N. Guay, and T. Schedler, Eds. Cham: Springer Nature; Birkhäuser,
2022, pp. 347–392.'
ista: 'Mirković I, Yang Y, Zhao G. 2022.Loop Grassmannians of Quivers and Affine
Quantum Groups. In: Representation Theory and Algebraic Geometry. Trends in Mathematics,
, 347–392.'
mla: Mirković, Ivan, et al. “Loop Grassmannians of Quivers and Affine Quantum Groups.”
Representation Theory and Algebraic Geometry, edited by Vladimir Baranovskky
et al., 1st ed., Springer Nature; Birkhäuser, 2022, pp. 347–92, doi:10.1007/978-3-030-82007-7_8.
short: I. Mirković, Y. Yang, G. Zhao, in:, V. Baranovskky, N. Guay, T. Schedler
(Eds.), Representation Theory and Algebraic Geometry, 1st ed., Springer Nature;
Birkhäuser, Cham, 2022, pp. 347–392.
date_created: 2023-01-16T10:06:41Z
date_published: 2022-06-16T00:00:00Z
date_updated: 2023-01-27T07:07:31Z
day: '16'
department:
- _id: TaHa
doi: 10.1007/978-3-030-82007-7_8
ec_funded: 1
edition: '1'
editor:
- first_name: Vladimir
full_name: Baranovskky, Vladimir
last_name: Baranovskky
- first_name: Nicolas
full_name: Guay, Nicolas
last_name: Guay
- first_name: Travis
full_name: Schedler, Travis
last_name: Schedler
external_id:
arxiv:
- '1810.10095'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1810.10095
month: '06'
oa: 1
oa_version: Preprint
page: 347-392
place: Cham
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Representation Theory and Algebraic Geometry
publication_identifier:
eisbn:
- '9783030820077'
eissn:
- 2297-024X
isbn:
- '9783030820060'
issn:
- 2297-0215
publication_status: published
publisher: Springer Nature; Birkhäuser
quality_controlled: '1'
scopus_import: '1'
series_title: TM
status: public
title: Loop Grassmannians of Quivers and Affine Quantum Groups
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '9977'
abstract:
- lang: eng
text: "For a Seifert fibered homology sphere X we show that the q-series invariant
Zˆ0(X; q) introduced by Gukov-Pei-Putrov-Vafa, is a resummation of the Ohtsuki
series Z0(X). We show that for every even k ∈ N there exists a full asymptotic
expansion of Zˆ0(X; q) for q tending to e 2πi/k, and in particular that the limit
Zˆ0(X; e 2πi/k) exists and is equal to the\r\nWRT quantum invariant τk(X). We
show that the poles of the Borel transform of Z0(X) coincide with the classical
complex Chern-Simons values, which we further show classifies the corresponding
components of the moduli space of flat SL(2, C)-connections."
acknowledgement: "We warmly thank S. Gukov for valuable discussions on the GPPV invariant
̂Z\U0001D44E(\U0001D4403; \U0001D45E). The first\r\nauthor was supported in part
by the center of excellence grant ‘Center for Quantum Geometry\r\nof Moduli Spaces’
from the Danish National Research Foundation (DNRF95) and by the ERCSynergy\r\ngrant
‘ReNewQuantum’. The second author received funding from the European Union’s Horizon
2020 research and innovation program under the Marie Skłodowska-Curie grant agreement
no. 754411."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: William
full_name: Mistegaard, William
id: 41B03CD0-62AE-11E9-84EF-0718E6697425
last_name: Mistegaard
- first_name: Jørgen Ellegaard
full_name: Andersen, Jørgen Ellegaard
last_name: Andersen
citation:
ama: Mistegaard W, Andersen JE. Resurgence analysis of quantum invariants of Seifert
fibered homology spheres. Journal of the London Mathematical Society. 2022;105(2):709-764.
doi:10.1112/jlms.12506
apa: Mistegaard, W., & Andersen, J. E. (2022). Resurgence analysis of quantum
invariants of Seifert fibered homology spheres. Journal of the London Mathematical
Society. Wiley. https://doi.org/10.1112/jlms.12506
chicago: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis
of Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the
London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12506.
ieee: W. Mistegaard and J. E. Andersen, “Resurgence analysis of quantum invariants
of Seifert fibered homology spheres,” Journal of the London Mathematical Society,
vol. 105, no. 2. Wiley, pp. 709–764, 2022.
ista: Mistegaard W, Andersen JE. 2022. Resurgence analysis of quantum invariants
of Seifert fibered homology spheres. Journal of the London Mathematical Society.
105(2), 709–764.
mla: Mistegaard, William, and Jørgen Ellegaard Andersen. “Resurgence Analysis of
Quantum Invariants of Seifert Fibered Homology Spheres.” Journal of the London
Mathematical Society, vol. 105, no. 2, Wiley, 2022, pp. 709–64, doi:10.1112/jlms.12506.
short: W. Mistegaard, J.E. Andersen, Journal of the London Mathematical Society
105 (2022) 709–764.
date_created: 2021-08-31T12:51:40Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2023-08-02T06:53:51Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12506
ec_funded: 1
external_id:
arxiv:
- '1811.05376'
isi:
- '000755205700001'
file:
- access_level: open_access
checksum: 9c72327d39f34f1a6eaa98fa4b8493f2
content_type: application/pdf
creator: dernst
date_created: 2022-03-24T11:42:25Z
date_updated: 2022-03-24T11:42:25Z
file_id: '10917'
file_name: 2022_JourLondonMathSoc_Andersen.pdf
file_size: 649130
relation: main_file
success: 1
file_date_updated: 2022-03-24T11:42:25Z
has_accepted_license: '1'
intvolume: ' 105'
isi: 1
issue: '2'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 709-764
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Resurgence analysis of quantum invariants of Seifert fibered homology spheres
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 105
year: '2022'
...
---
_id: '10704'
abstract:
- lang: eng
text: We define and study the existence of very stable Higgs bundles on Riemann
surfaces, how it implies a precise formula for the multiplicity of the very stable
components of the global nilpotent cone and its relationship to mirror symmetry.
The main ingredients are the Bialynicki-Birula theory of C∗-actions on semiprojective
varieties, C∗ characters of indices of C∗-equivariant coherent sheaves, Hecke
transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin
fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs
bundles.
acknowledgement: We would like to thank Brian Collier, Davide Gaiotto, Peter Gothen,
Jochen Heinloth, Daniel Huybrechts, Quoc Ho, Joel Kamnitzer, Gérard Laumon, Luca
Migliorini, Alexander Minets, Brent Pym, Peng Shan, Carlos Simpson, András Szenes,
Fernando R. Villegas, Richard Wentworth, Edward Witten and Kōta Yoshioka for interesting
comments and discussions. Most of all we are grateful for a long list of very helpful
comments by the referee. We would also like to thank the organizers of the Summer
School on Higgs bundles in Hamburg in September 2018, where the authors and Richard
Wentworth were giving lectures and where the work in this paper started by considering
the mirror of the Lagrangian upward flows W+E investigated in [17]. The second author
wishes to thank EPSRC and ICMAT for support. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Nigel
full_name: Hitchin, Nigel
last_name: Hitchin
citation:
ama: Hausel T, Hitchin N. Very stable Higgs bundles, equivariant multiplicity and
mirror symmetry. Inventiones Mathematicae. 2022;228:893-989. doi:10.1007/s00222-021-01093-7
apa: Hausel, T., & Hitchin, N. (2022). Very stable Higgs bundles, equivariant
multiplicity and mirror symmetry. Inventiones Mathematicae. Springer Nature.
https://doi.org/10.1007/s00222-021-01093-7
chicago: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant
Multiplicity and Mirror Symmetry.” Inventiones Mathematicae. Springer Nature,
2022. https://doi.org/10.1007/s00222-021-01093-7.
ieee: T. Hausel and N. Hitchin, “Very stable Higgs bundles, equivariant multiplicity
and mirror symmetry,” Inventiones Mathematicae, vol. 228. Springer Nature,
pp. 893–989, 2022.
ista: Hausel T, Hitchin N. 2022. Very stable Higgs bundles, equivariant multiplicity
and mirror symmetry. Inventiones Mathematicae. 228, 893–989.
mla: Hausel, Tamás, and Nigel Hitchin. “Very Stable Higgs Bundles, Equivariant Multiplicity
and Mirror Symmetry.” Inventiones Mathematicae, vol. 228, Springer Nature,
2022, pp. 893–989, doi:10.1007/s00222-021-01093-7.
short: T. Hausel, N. Hitchin, Inventiones Mathematicae 228 (2022) 893–989.
date_created: 2022-01-30T23:01:34Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-02T14:03:20Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00222-021-01093-7
external_id:
arxiv:
- '2101.08583'
isi:
- '000745495400001'
file:
- access_level: open_access
checksum: a382ba75acebc9adfb8fe56247cb410e
content_type: application/pdf
creator: dernst
date_created: 2023-02-27T07:30:47Z
date_updated: 2023-02-27T07:30:47Z
file_id: '12687'
file_name: 2022_InventionesMahtematicae_Hausel.pdf
file_size: 1069538
relation: main_file
success: 1
file_date_updated: 2023-02-27T07:30:47Z
has_accepted_license: '1'
intvolume: ' 228'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 893-989
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- description: News on the ISTA Website
relation: press_release
url: https://ista.ac.at/en/news/the-tip-of-the-mathematical-iceberg/
scopus_import: '1'
status: public
title: Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 228
year: '2022'
...
---
_id: '10772'
abstract:
- lang: eng
text: We introduce tropical corals, balanced trees in a half-space, and show that
they correspond to holomorphic polygons capturing the product rule in Lagrangian
Floer theory for the elliptic curve. We then prove a correspondence theorem equating
counts of tropical corals to punctured log Gromov–Witten invariants of the Tate
curve. This implies that the homogeneous coordinate ring of the mirror to the
Tate curve is isomorphic to the degree-zero part of symplectic cohomology, confirming
a prediction of homological mirror symmetry.
acknowledgement: 'This paper is based on my PhD thesis, which would not be possible
without the support of my advisor Bernd Siebert. I also thank Dan Abramovich, Mohammed
Abouzaid, Mark Gross, Tom Coates and Dimitri Zvonkine for many useful conversations.
Finally, I thank the anonymous referees for their many insightful comments and valuable
suggestions which have resulted in major improvements to this article. This project
has received funding from the EuropeanResearch Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement Number:
682603), and from Fondation Mathématique Jacques Hadamard. '
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Nuroemuer Huelya
full_name: Arguez, Nuroemuer Huelya
id: 3c26b22e-c843-11eb-aa56-d38ffa0bdd08
last_name: Arguez
citation:
ama: Arguez NH. Mirror symmetry for the Tate curve via tropical and log corals.
Journal of the London Mathematical Society. 2022;105(1):343-411. doi:10.1112/jlms.12515
apa: Arguez, N. H. (2022). Mirror symmetry for the Tate curve via tropical and log
corals. Journal of the London Mathematical Society. London Mathematical
Society. https://doi.org/10.1112/jlms.12515
chicago: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical
and Log Corals.” Journal of the London Mathematical Society. London Mathematical
Society, 2022. https://doi.org/10.1112/jlms.12515.
ieee: N. H. Arguez, “Mirror symmetry for the Tate curve via tropical and log corals,”
Journal of the London Mathematical Society, vol. 105, no. 1. London Mathematical
Society, pp. 343–411, 2022.
ista: Arguez NH. 2022. Mirror symmetry for the Tate curve via tropical and log corals.
Journal of the London Mathematical Society. 105(1), 343–411.
mla: Arguez, Nuroemuer Huelya. “Mirror Symmetry for the Tate Curve via Tropical
and Log Corals.” Journal of the London Mathematical Society, vol. 105,
no. 1, London Mathematical Society, 2022, pp. 343–411, doi:10.1112/jlms.12515.
short: N.H. Arguez, Journal of the London Mathematical Society 105 (2022) 343–411.
date_created: 2022-02-20T23:01:33Z
date_published: 2022-02-05T00:00:00Z
date_updated: 2023-08-02T14:29:50Z
day: '05'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12515
external_id:
arxiv:
- '1712.10260'
isi:
- '000751600600001'
file:
- access_level: open_access
checksum: 8bd0fd9694be894a191857ddf27678f0
content_type: application/pdf
creator: dernst
date_created: 2022-02-21T11:22:58Z
date_updated: 2022-02-21T11:22:58Z
file_id: '10783'
file_name: 2022_JournLondonMathSociety_Arguez.pdf
file_size: 936873
relation: main_file
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intvolume: ' 105'
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issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '02'
oa: 1
oa_version: Published Version
page: 343-411
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mirror symmetry for the Tate curve via tropical and log corals
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 105
year: '2022'
...
---
_id: '12793'
abstract:
- lang: eng
text: "Let F be a global function field with constant field Fq. Let G be a reductive
group over Fq. We establish a variant of Arthur's truncated kernel for G and for
its Lie algebra which generalizes Arthur's original construction. We establish
a coarse geometric expansion for our variant truncation.\r\nAs applications, we
consider some existence and uniqueness problems of some cuspidal automorphic representations
for the functions field of the projective line P1Fq with two points of ramifications."
acknowledgement: 'I’d like to thank Prof. Chaudouard for introducing me to this area.
I’d like to thank Prof. Harris for asking me the question that makes Section 10
possible. I’m grateful for the support of Prof. Hausel and IST Austria. The author
was funded by an ISTplus fellowship: This project has received funding from the
European Union’s Horizon 2020 research and innovation programme under the Marie
Skłodowska-Curie Grant Agreement No. 754411.'
article_processing_charge: No
article_type: original
author:
- first_name: Hongjie
full_name: Yu, Hongjie
id: 3D7DD9BE-F248-11E8-B48F-1D18A9856A87
last_name: Yu
orcid: 0000-0001-5128-7126
citation:
ama: Yu H. A coarse geometric expansion of a variant of Arthur’s truncated traces
and some applications. Pacific Journal of Mathematics. 2022;321(1):193-237.
doi:10.2140/pjm.2022.321.193
apa: Yu, H. (2022). A coarse geometric expansion of a variant of Arthur’s truncated
traces and some applications. Pacific Journal of Mathematics. Mathematical
Sciences Publishers. https://doi.org/10.2140/pjm.2022.321.193
chicago: Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated
Traces and Some Applications.” Pacific Journal of Mathematics. Mathematical
Sciences Publishers, 2022. https://doi.org/10.2140/pjm.2022.321.193.
ieee: H. Yu, “ A coarse geometric expansion of a variant of Arthur’s truncated traces
and some applications,” Pacific Journal of Mathematics, vol. 321, no. 1.
Mathematical Sciences Publishers, pp. 193–237, 2022.
ista: Yu H. 2022. A coarse geometric expansion of a variant of Arthur’s truncated
traces and some applications. Pacific Journal of Mathematics. 321(1), 193–237.
mla: Yu, Hongjie. “ A Coarse Geometric Expansion of a Variant of Arthur’s Truncated
Traces and Some Applications.” Pacific Journal of Mathematics, vol. 321,
no. 1, Mathematical Sciences Publishers, 2022, pp. 193–237, doi:10.2140/pjm.2022.321.193.
short: H. Yu, Pacific Journal of Mathematics 321 (2022) 193–237.
date_created: 2023-04-02T22:01:11Z
date_published: 2022-08-29T00:00:00Z
date_updated: 2023-08-04T10:42:38Z
day: '29'
department:
- _id: TaHa
doi: 10.2140/pjm.2022.321.193
ec_funded: 1
external_id:
arxiv:
- '2109.10245'
isi:
- '000954466300006'
intvolume: ' 321'
isi: 1
issue: '1'
keyword:
- Arthur–Selberg trace formula
- cuspidal automorphic representations
- global function fields
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2109.10245
month: '08'
oa: 1
oa_version: Preprint
page: 193-237
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Pacific Journal of Mathematics
publication_identifier:
eissn:
- 1945-5844
issn:
- 0030-8730
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: ' A coarse geometric expansion of a variant of Arthur''s truncated traces and
some applications'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 321
year: '2022'
...
---
_id: '6965'
abstract:
- lang: eng
text: The central object of investigation of this paper is the Hirzebruch class,
a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The
generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following
the work of Weber, we investigate its equivariant version for (possibly singular)
toric varieties. The local decomposition of the Hirzebruch class to the fixed
points of the torus action and a formula for the local class in terms of the defining
fan are recalled. After this review part, we prove the positivity of local Hirzebruch
classes for all toric varieties, thus proving false the alleged counterexample
given by Weber.
article_processing_charge: No
article_type: original
author:
- first_name: Kamil P
full_name: Rychlewicz, Kamil P
id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
last_name: Rychlewicz
citation:
ama: Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric
varieties. Bulletin of the London Mathematical Society. 2021;53(2):560-574.
doi:10.1112/blms.12442
apa: Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class
for toric varieties. Bulletin of the London Mathematical Society. Wiley.
https://doi.org/10.1112/blms.12442
chicago: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
for Toric Varieties.” Bulletin of the London Mathematical Society. Wiley,
2021. https://doi.org/10.1112/blms.12442.
ieee: K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for
toric varieties,” Bulletin of the London Mathematical Society, vol. 53,
no. 2. Wiley, pp. 560–574, 2021.
ista: Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class
for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574.
mla: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
for Toric Varieties.” Bulletin of the London Mathematical Society, vol.
53, no. 2, Wiley, 2021, pp. 560–74, doi:10.1112/blms.12442.
short: K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574.
date_created: 2019-10-24T08:04:09Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-08-04T10:43:39Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/blms.12442
external_id:
arxiv:
- '1910.10435'
isi:
- '000594805800001'
intvolume: ' 53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.10435
month: '04'
oa: 1
oa_version: Preprint
page: 560-574
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- 1469-2120
issn:
- 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: The positivity of local equivariant Hirzebruch class for toric varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2021'
...
---
_id: '9099'
abstract:
- lang: eng
text: We show that on an Abelian variety over an algebraically closed field of positive
characteristic, the obstruction to lifting an automorphism to a field of characteristic
zero as a morphism vanishes if and only if it vanishes for lifting it as a derived
autoequivalence. We also compare the deformation space of these two types of deformations.
acknowledgement: I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina
Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas
Hausel for hosting me in his research group at IST Austria, and the referees for
their valuable suggestions. This research has received funding from the European
Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie
Grant Agreement No. 754411.
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. Lifting automorphisms on Abelian varieties as derived autoequivalences.
Archiv der Mathematik. 2021;116(5):515-527. doi:10.1007/s00013-020-01564-y
apa: Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived
autoequivalences. Archiv Der Mathematik. Springer Nature. https://doi.org/10.1007/s00013-020-01564-y
chicago: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
Autoequivalences.” Archiv Der Mathematik. Springer Nature, 2021. https://doi.org/10.1007/s00013-020-01564-y.
ieee: T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,”
Archiv der Mathematik, vol. 116, no. 5. Springer Nature, pp. 515–527, 2021.
ista: Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived
autoequivalences. Archiv der Mathematik. 116(5), 515–527.
mla: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
Autoequivalences.” Archiv Der Mathematik, vol. 116, no. 5, Springer Nature,
2021, pp. 515–27, doi:10.1007/s00013-020-01564-y.
short: T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527.
date_created: 2021-02-07T23:01:13Z
date_published: 2021-05-01T00:00:00Z
date_updated: 2023-08-07T13:42:38Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00013-020-01564-y
ec_funded: 1
external_id:
arxiv:
- '2001.07762'
isi:
- '000612580200001'
intvolume: ' 116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2001.07762
month: '05'
oa: 1
oa_version: Preprint
page: 515-527
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Archiv der Mathematik
publication_identifier:
eissn:
- '14208938'
issn:
- 0003889X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lifting automorphisms on Abelian varieties as derived autoequivalences
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 116
year: '2021'
...
---
_id: '9173'
abstract:
- lang: eng
text: We show that Hilbert schemes of points on supersingular Enriques surface in
characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties
but are not irreducible symplectic as the hodge number h2,0 > 1, even though a
supersingular Enriques surface is an irreducible symplectic variety. These are
the classes of varieties which appear only in characteristic 2 and they show that
the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic
2. It also gives examples of varieties with trivial canonical class which are
neither irreducible symplectic nor Calabi-Yau, thereby showing that there are
strictly more classes of simply connected varieties with trivial canonical class
in characteristic 2 than over C as given by Beauville-Bogolomov decomposition
theorem.
acknowledgement: I would like to thank M. Zdanwociz for various mathematical discussions
which lead to this article, Tamas Hausel for hosting me in his research group at
IST Austria and the anonymous referee for their helpful suggestions and comments.
This research has received funding from the European Union's Horizon 2020 Marie
Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology
Austria IST-PLUS Grant No. 754411.
article_number: '102957'
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface. Bulletin des Sciences Mathematiques. 2021;167(03). doi:10.1016/j.bulsci.2021.102957
apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a
supersingular Enriques surface. Bulletin Des Sciences Mathematiques. Elsevier.
https://doi.org/10.1016/j.bulsci.2021.102957
chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a
Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques. Elsevier,
2021. https://doi.org/10.1016/j.bulsci.2021.102957.
ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface,” Bulletin des Sciences Mathematiques, vol. 167, no. 03.
Elsevier, 2021.
ista: Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular
Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.
mla: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular
Enriques Surface.” Bulletin Des Sciences Mathematiques, vol. 167, no. 03,
102957, Elsevier, 2021, doi:10.1016/j.bulsci.2021.102957.
short: T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).
date_created: 2021-02-21T23:01:20Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-07T13:47:48Z
day: '01'
department:
- _id: TaHa
doi: 10.1016/j.bulsci.2021.102957
ec_funded: 1
external_id:
arxiv:
- '2010.08976'
isi:
- '000623881600009'
intvolume: ' 167'
isi: 1
issue: '03'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2010.08976
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Bulletin des Sciences Mathematiques
publication_identifier:
issn:
- 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pathologies of the Hilbert scheme of points of a supersingular Enriques surface
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 167
year: '2021'
...
---
_id: '9359'
abstract:
- lang: eng
text: "We prove that the factorization homologies of a scheme with coefficients
in truncated polynomial algebras compute the cohomologies of its generalized configuration
spaces. Using Koszul duality between commutative algebras and Lie algebras, we
obtain new expressions for the cohomologies of the latter. As a consequence, we
obtain a uniform and conceptual approach for treating homological stability, homological
densities, and arithmetic densities of generalized configuration spaces. Our results
categorify, generalize, and in fact provide a conceptual understanding of the
coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of
the stable homological densities also yields rational homotopy types, answering
a question posed by Vakil--Wood. Our approach hinges on the study of homological
stability of cohomological Chevalley complexes, which is of independent interest.\r\n"
acknowledgement: "This paper owes an obvious intellectual debt to the illuminating
treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie
in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing
the question of explaining coincidences in homological densities to his attention.
Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the
subject, O. Randal-Williams for many comments which\r\ngreatly help improve the
exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally,
the author is grateful to the anonymous referee for carefully reading the manuscript
and for providing\r\nnumerous comments which greatly helped improve the clarity
and precision of the exposition.\r\nThis work is supported by the Advanced Grant
“Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research
Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,”
Austrian Science Fund (FWF): M 2751."
article_processing_charge: No
article_type: original
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
citation:
ama: Ho QP. Homological stability and densities of generalized configuration spaces.
Geometry & Topology. 2021;25(2):813-912. doi:10.2140/gt.2021.25.813
apa: Ho, Q. P. (2021). Homological stability and densities of generalized configuration
spaces. Geometry & Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2021.25.813
chicago: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology. Mathematical Sciences Publishers, 2021.
https://doi.org/10.2140/gt.2021.25.813.
ieee: Q. P. Ho, “Homological stability and densities of generalized configuration
spaces,” Geometry & Topology, vol. 25, no. 2. Mathematical Sciences
Publishers, pp. 813–912, 2021.
ista: Ho QP. 2021. Homological stability and densities of generalized configuration
spaces. Geometry & Topology. 25(2), 813–912.
mla: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology, vol. 25, no. 2, Mathematical Sciences
Publishers, 2021, pp. 813–912, doi:10.2140/gt.2021.25.813.
short: Q.P. Ho, Geometry & Topology 25 (2021) 813–912.
date_created: 2021-05-02T06:59:33Z
date_published: 2021-04-27T00:00:00Z
date_updated: 2023-08-08T13:28:59Z
day: '27'
ddc:
- '514'
- '516'
- '512'
department:
- _id: TaHa
doi: 10.2140/gt.2021.25.813
ec_funded: 1
external_id:
arxiv:
- '1802.07948'
isi:
- '000682738600005'
file:
- access_level: open_access
checksum: 643a8d2d6f06f0888dcd7503f55d0920
content_type: application/pdf
creator: qho
date_created: 2021-05-03T06:54:06Z
date_updated: 2021-05-03T06:54:06Z
file_id: '9366'
file_name: densities.pdf
file_size: 479268
relation: main_file
success: 1
file_date_updated: 2021-05-03T06:54:06Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '2'
keyword:
- Generalized configuration spaces
- homological stability
- homological densities
- chiral algebras
- chiral homology
- factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '04'
oa: 1
oa_version: Submitted Version
page: 813-912
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
publication: Geometry & Topology
publication_identifier:
issn:
- 1364-0380
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
status: public
title: Homological stability and densities of generalized configuration spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2021'
...
---
_id: '9998'
abstract:
- lang: eng
text: We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss
type A in detail as well as its connections with quantum XXZ spin chains and trigonometric
Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic
version of results of Givental and Kim, connecting quantum geometry of flag varieties
and Toda lattice.
acknowledgement: 'First of all we would like to thank Andrei Okounkov for invaluable
discussions, advises and sharing with us his fantastic viewpoint on modern quantum
geometry. We are also grateful to D. Korb and Z. Zhou for their interest and comments.
The work of A. Smirnov was supported in part by RFBR Grants under Numbers 15-02-04175
and 15-01-04217 and in part by NSF Grant DMS–2054527. The work of P. Koroteev, A.M.
Zeitlin and A. Smirnov is supported in part by AMS Simons travel Grant. A. M. Zeitlin
is partially supported by Simons Collaboration Grant, Award ID: 578501. Open access
funding provided by Institute of Science and Technology (IST Austria).'
article_number: '87'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Peter
full_name: Koroteev, Peter
last_name: Koroteev
- first_name: Petr
full_name: Pushkar, Petr
id: 151DCEB6-9EC3-11E9-8480-ABECE5697425
last_name: Pushkar
- first_name: Andrey V.
full_name: Smirnov, Andrey V.
last_name: Smirnov
- first_name: Anton M.
full_name: Zeitlin, Anton M.
last_name: Zeitlin
citation:
ama: Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties
and many-body systems. Selecta Mathematica. 2021;27(5). doi:10.1007/s00029-021-00698-3
apa: Koroteev, P., Pushkar, P., Smirnov, A. V., & Zeitlin, A. M. (2021). Quantum
K-theory of quiver varieties and many-body systems. Selecta Mathematica.
Springer Nature. https://doi.org/10.1007/s00029-021-00698-3
chicago: Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin.
“Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica.
Springer Nature, 2021. https://doi.org/10.1007/s00029-021-00698-3.
ieee: P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory
of quiver varieties and many-body systems,” Selecta Mathematica, vol. 27,
no. 5. Springer Nature, 2021.
ista: Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver
varieties and many-body systems. Selecta Mathematica. 27(5), 87.
mla: Koroteev, Peter, et al. “Quantum K-Theory of Quiver Varieties and Many-Body
Systems.” Selecta Mathematica, vol. 27, no. 5, 87, Springer Nature, 2021,
doi:10.1007/s00029-021-00698-3.
short: P. Koroteev, P. Pushkar, A.V. Smirnov, A.M. Zeitlin, Selecta Mathematica
27 (2021).
date_created: 2021-09-12T22:01:22Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-14T06:34:14Z
day: '30'
ddc:
- '530'
department:
- _id: TaHa
doi: 10.1007/s00029-021-00698-3
external_id:
isi:
- '000692795200001'
file:
- access_level: open_access
checksum: beadc5a722ffb48190e1e63ee2dbfee5
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-13T11:31:34Z
date_updated: 2021-09-13T11:31:34Z
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file_name: 2021_SelectaMath_Koroteev.pdf
file_size: 584648
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file_date_updated: 2021-09-13T11:31:34Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
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language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Selecta Mathematica
publication_identifier:
eissn:
- 1420-9020
issn:
- 1022-1824
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum K-theory of quiver varieties and many-body systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2021'
...
---
_id: '10033'
abstract:
- lang: eng
text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not
pro-nilpotent in the sense of [3]. However, under some connectivity assumptions,
we prove that Koszul duality induces an equivalence of categories and that this
equivalence behaves nicely with respect to Verdier duality on the Ran space and
integrating along the Ran space, i.e. taking factorization homology. Based on
ideas sketched in [4], we show that these results also offer a simpler alternative
to one of the two main steps in the proof of the Atiyah-Bott formula given in
[7] and [5].
acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory,
without whose tireless guidance and encouragement in pursuing this problem, this
work would not have been possible. The author is grateful to his advisor B.C. Ngô
for many years of patient guidance and support. This paper is revised while the
author is a postdoc in Hausel group at IST Austria. We thank him and the group for
providing a wonderful research environment. The author also gratefully acknowledges
the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization
Homology,” Austrian Science Fund (FWF): M 2751.'
article_number: '107992'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
orcid: 0000-0001-6889-1418
citation:
ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances
in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992
apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul
duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992
chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul
Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992.
ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,”
Advances in Mathematics, vol. 392. Elsevier, 2021.
ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality.
Advances in Mathematics. 392, 107992.
mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.”
Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992.
short: Q.P. Ho, Advances in Mathematics 392 (2021).
date_created: 2021-09-21T15:58:59Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2023-08-14T06:54:35Z
day: '21'
ddc:
- '514'
department:
- _id: TaHa
doi: 10.1016/j.aim.2021.107992
external_id:
arxiv:
- '1610.00212'
isi:
- '000707040300031'
file:
- access_level: open_access
checksum: f3c0086d41af11db31c00014efb38072
content_type: application/pdf
creator: qho
date_created: 2021-09-21T15:58:52Z
date_updated: 2021-09-21T15:58:52Z
file_id: '10034'
file_name: 1-s2.0-S000187082100431X-main.pdf
file_size: 840635
relation: main_file
file_date_updated: 2021-09-21T15:58:52Z
has_accepted_license: '1'
intvolume: ' 392'
isi: 1
keyword:
- Chiral algebras
- Chiral homology
- Factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
publication: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Atiyah-Bott formula and connectivity in chiral Koszul duality
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 392
year: '2021'
...
---
_id: '7004'
abstract:
- lang: eng
text: We define an action of the (double of) Cohomological Hall algebra of Kontsevich
and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov.
We identify this action with the one of the affine Yangian of gl(1). Based on
that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák.
We conjecture that our approach works for a big class of Calabi–Yau categories,
including those associated with toric Calabi–Yau 3-folds.
article_processing_charge: No
article_type: original
author:
- first_name: Miroslav
full_name: Rapcak, Miroslav
last_name: Rapcak
- first_name: Yan
full_name: Soibelman, Yan
last_name: Soibelman
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex
algebras and instantons. Communications in Mathematical Physics. 2020;376:1803-1873.
doi:10.1007/s00220-019-03575-5
apa: Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2020). Cohomological Hall
algebras, vertex algebras and instantons. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-019-03575-5
chicago: Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological
Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical
Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03575-5.
ieee: M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras,
vertex algebras and instantons,” Communications in Mathematical Physics,
vol. 376. Springer Nature, pp. 1803–1873, 2020.
ista: Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras,
vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.
mla: Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and
Instantons.” Communications in Mathematical Physics, vol. 376, Springer
Nature, 2020, pp. 1803–73, doi:10.1007/s00220-019-03575-5.
short: M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical
Physics 376 (2020) 1803–1873.
date_created: 2019-11-12T14:01:27Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-17T14:02:59Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00220-019-03575-5
ec_funded: 1
external_id:
arxiv:
- '1810.10402'
isi:
- '000536255500004'
intvolume: ' 376'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.10402
month: '06'
oa: 1
oa_version: Preprint
page: 1803-1873
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras, vertex algebras and instantons
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 376
year: '2020'
...
---
_id: '7683'
abstract:
- lang: eng
text: For any free oriented Borel–Moore homology theory A, we construct an associative
product on the A-theory of the stack of Higgs torsion sheaves over a projective
curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation,
and prove it is faithful when A is replaced with usual Borel–Moore homology groups.
We also introduce moduli spaces of stable triples, heavily inspired by Nakajima
quiver varieties, whose A-theory admits an AHa0C-action. These triples can be
interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action
of AHa0C on the cohomology of Hilbert schemes of points on T∗C.
article_number: '30'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sasha
full_name: Minets, Sasha
id: 3E7C5304-F248-11E8-B48F-1D18A9856A87
last_name: Minets
orcid: 0000-0003-3883-1806
citation:
ama: Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of
triples and sheaves on surfaces. Selecta Mathematica, New Series. 2020;26(2).
doi:10.1007/s00029-020-00553-x
apa: Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces. Selecta Mathematica, New Series. Springer
Nature. https://doi.org/10.1007/s00029-020-00553-x
chicago: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves,
Moduli of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series.
Springer Nature, 2020. https://doi.org/10.1007/s00029-020-00553-x.
ieee: S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces,” Selecta Mathematica, New Series, vol.
26, no. 2. Springer Nature, 2020.
ista: Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli
of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30.
mla: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli
of Triples and Sheaves on Surfaces.” Selecta Mathematica, New Series, vol.
26, no. 2, 30, Springer Nature, 2020, doi:10.1007/s00029-020-00553-x.
short: S. Minets, Selecta Mathematica, New Series 26 (2020).
date_created: 2020-04-26T22:00:44Z
date_published: 2020-04-15T00:00:00Z
date_updated: 2023-08-21T06:14:58Z
day: '15'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00029-020-00553-x
external_id:
arxiv:
- '1801.01429'
isi:
- '000526036400001'
file:
- access_level: open_access
checksum: 2368c4662629b4759295eb365323b2ad
content_type: application/pdf
creator: dernst
date_created: 2020-04-28T10:57:58Z
date_updated: 2020-07-14T12:48:02Z
file_id: '7690'
file_name: 2020_SelectaMathematica_Minets.pdf
file_size: 792469
relation: main_file
file_date_updated: 2020-07-14T12:48:02Z
has_accepted_license: '1'
intvolume: ' 26'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Selecta Mathematica, New Series
publication_identifier:
eissn:
- '14209020'
issn:
- '10221824'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and
sheaves on surfaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2020'
...
---
_id: '7940'
abstract:
- lang: eng
text: We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody
Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter
is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras.
As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this
class of affine Yangians. Another independent proof of the PBW theorem is given
recently by Guay, Regelskis, and Wendlandt [GRW18].
acknowledgement: Gufang Zhao is affiliated to IST Austria, Hausel group until July
of 2018. Supported by the Advanced Grant Arithmetic and Physics of Higgs moduli
spaces No. 320593 of the European Research Council.
article_processing_charge: No
article_type: original
author:
- first_name: Yaping
full_name: Yang, Yaping
id: 360D8648-F248-11E8-B48F-1D18A9856A87
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The PBW theorem for affine Yangians. Transformation Groups.
2020;25:1371-1385. doi:10.1007/s00031-020-09572-6
apa: Yang, Y., & Zhao, G. (2020). The PBW theorem for affine Yangians. Transformation
Groups. Springer Nature. https://doi.org/10.1007/s00031-020-09572-6
chicago: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups. Springer Nature, 2020. https://doi.org/10.1007/s00031-020-09572-6.
ieee: Y. Yang and G. Zhao, “The PBW theorem for affine Yangians,” Transformation
Groups, vol. 25. Springer Nature, pp. 1371–1385, 2020.
ista: Yang Y, Zhao G. 2020. The PBW theorem for affine Yangians. Transformation
Groups. 25, 1371–1385.
mla: Yang, Yaping, and Gufang Zhao. “The PBW Theorem for Affine Yangians.” Transformation
Groups, vol. 25, Springer Nature, 2020, pp. 1371–85, doi:10.1007/s00031-020-09572-6.
short: Y. Yang, G. Zhao, Transformation Groups 25 (2020) 1371–1385.
date_created: 2020-06-07T22:00:55Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-08-21T07:06:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00031-020-09572-6
ec_funded: 1
external_id:
arxiv:
- '1804.04375'
isi:
- '000534874300003'
intvolume: ' 25'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.04375
month: '12'
oa: 1
oa_version: Preprint
page: 1371-1385
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Transformation Groups
publication_identifier:
eissn:
- 1531586X
issn:
- '10834362'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The PBW theorem for affine Yangians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2020'
...
---
_id: '8325'
abstract:
- lang: eng
text: "Let \U0001D439:ℤ2→ℤ be the pointwise minimum of several linear functions.
The theory of smoothing allows us to prove that under certain conditions there
exists the pointwise minimal function among all integer-valued superharmonic functions
coinciding with F “at infinity”. We develop such a theory to prove existence of
so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo,
G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the
phenomena of the identity in the sandpile group for planar domains where solitons
appear according to experiments. We prove that sandpile states, defined using
our smoothing procedure, move changeless when we apply the wave operator (that
is why we call them solitons), and can interact, forming triads and nodes. "
acknowledgement: We thank Andrea Sportiello for sharing his insights on perturbative
regimes of the Abelian sandpile model which was the starting point of our work.
We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We
thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who
participated on the initial state of this project, when we had nothing except the
computer simulation and pictures. We thank Mikhail Raskin for providing us the code
on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max
Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak,
Danila Cherkashin asked us a lot of questions and listened to us; not all of their
questions found answers here, but we are going to treat them in subsequent papers.
article_processing_charge: No
article_type: original
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions.
Communications in Mathematical Physics. 2020;378(9):1649-1675. doi:10.1007/s00220-020-03828-8
apa: Kalinin, N., & Shkolnikov, M. (2020). Sandpile solitons via smoothing of
superharmonic functions. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-020-03828-8
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing
of Superharmonic Functions.” Communications in Mathematical Physics. Springer
Nature, 2020. https://doi.org/10.1007/s00220-020-03828-8.
ieee: N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic
functions,” Communications in Mathematical Physics, vol. 378, no. 9. Springer
Nature, pp. 1649–1675, 2020.
ista: Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic
functions. Communications in Mathematical Physics. 378(9), 1649–1675.
mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of
Superharmonic Functions.” Communications in Mathematical Physics, vol.
378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:10.1007/s00220-020-03828-8.
short: N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020)
1649–1675.
date_created: 2020-08-30T22:01:13Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-08-22T09:00:03Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00220-020-03828-8
ec_funded: 1
external_id:
arxiv:
- '1711.04285'
isi:
- '000560620600001'
intvolume: ' 378'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1711.04285
month: '09'
oa: 1
oa_version: Preprint
page: 1649-1675
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- '14320916'
issn:
- '00103616'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sandpile solitons via smoothing of superharmonic functions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 378
year: '2020'
...
---
_id: '8539'
abstract:
- lang: eng
text: Cohomological and K-theoretic stable bases originated from the study of quantum
cohomology and quantum K-theory. Restriction formula for cohomological stable
bases played an important role in computing the quantum connection of cotangent
bundle of partial flag varieties. In this paper we study the K-theoretic stable
bases of cotangent bundles of flag varieties. We describe these bases in terms
of the action of the affine Hecke algebra and the twisted group algebra of KostantKumar.
Using this algebraic description and the method of root polynomials, we give a
restriction formula of the stable bases. We apply it to obtain the restriction
formula for partial flag varieties. We also build a relation between the stable
basis and the Casselman basis in the principal series representations of the Langlands
dual group. As an application, we give a closed formula for the transition matrix
between Casselman basis and the characteristic functions.
- lang: fre
text: "Les bases stables cohomologiques et K-théoriques proviennent de l’étude de
la cohomologie quantique et de la K-théorie quantique. La formule de restriction
pour les bases stables cohomologiques a joué un rôle important dans le calcul
de la connexion quantique du fibré cotangent de variétés de drapeaux partielles.
Dans cet article, nous étudions les bases stables K-théoriques de fibré cotangents
des variétés de drapeaux. Nous décrivons ces bases en fonction de l’action de
l’algèbre de Hecke affine et de l’algèbre de Kostant-Kumar. En utilisant cette
description algébrique et la méthode des polynômes de racine, nous donnons une
formule de restriction des bases stables. Nous l’appliquons\r\npour obtenir la
formule de restriction pour les variétés de drapeaux partielles. Nous construisons
également une relation entre la base stable et la base de Casselman dans les représentations
de la série principale du groupe dual de Langlands p-adique. Comme une application,
nous donnons une formule close pour la matrice de transition entre la base de
Casselman et les fonctions caractéristiques. "
article_processing_charge: No
article_type: original
author:
- first_name: C.
full_name: Su, C.
last_name: Su
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
- first_name: C.
full_name: Zhong, C.
last_name: Zhong
citation:
ama: Su C, Zhao G, Zhong C. On the K-theory stable bases of the springer resolution.
Annales Scientifiques de l’Ecole Normale Superieure. 2020;53(3):663-671.
doi:10.24033/asens.2431
apa: Su, C., Zhao, G., & Zhong, C. (2020). On the K-theory stable bases of the
springer resolution. Annales Scientifiques de l’Ecole Normale Superieure.
Société Mathématique de France. https://doi.org/10.24033/asens.2431
chicago: Su, C., Gufang Zhao, and C. Zhong. “On the K-Theory Stable Bases of the
Springer Resolution.” Annales Scientifiques de l’Ecole Normale Superieure.
Société Mathématique de France, 2020. https://doi.org/10.24033/asens.2431.
ieee: C. Su, G. Zhao, and C. Zhong, “On the K-theory stable bases of the springer
resolution,” Annales Scientifiques de l’Ecole Normale Superieure, vol.
53, no. 3. Société Mathématique de France, pp. 663–671, 2020.
ista: Su C, Zhao G, Zhong C. 2020. On the K-theory stable bases of the springer
resolution. Annales Scientifiques de l’Ecole Normale Superieure. 53(3), 663–671.
mla: Su, C., et al. “On the K-Theory Stable Bases of the Springer Resolution.” Annales
Scientifiques de l’Ecole Normale Superieure, vol. 53, no. 3, Société Mathématique
de France, 2020, pp. 663–71, doi:10.24033/asens.2431.
short: C. Su, G. Zhao, C. Zhong, Annales Scientifiques de l’Ecole Normale Superieure
53 (2020) 663–671.
date_created: 2020-09-20T22:01:38Z
date_published: 2020-06-01T00:00:00Z
date_updated: 2023-08-22T09:27:57Z
day: '01'
department:
- _id: TaHa
doi: 10.24033/asens.2431
external_id:
arxiv:
- '1708.08013'
isi:
- '000592182600004'
intvolume: ' 53'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.08013
month: '06'
oa: 1
oa_version: Preprint
page: 663-671
publication: Annales Scientifiques de l'Ecole Normale Superieure
publication_identifier:
issn:
- 0012-9593
publication_status: published
publisher: Société Mathématique de France
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the K-theory stable bases of the springer resolution
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2020'
...
---
_id: '15070'
abstract:
- lang: eng
text: This workshop focused on interactions between the various perspectives on
the moduli space of Higgs bundles over a Riemann surface. This subject draws on
algebraic geometry, geometric topology, geometric analysis and mathematical physics,
and the goal was to promote interactions between these various branches of the
subject. The main current directions of research were well represented by the
participants, and the talks included many from both senior and junior participants.
article_processing_charge: No
article_type: original
author:
- first_name: Lara
full_name: Anderson, Lara
last_name: Anderson
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Rafe
full_name: Mazzeo, Rafe
last_name: Mazzeo
- first_name: Laura
full_name: Schaposnik, Laura
last_name: Schaposnik
citation:
ama: Anderson L, Hausel T, Mazzeo R, Schaposnik L. Geometry and physics of Higgs
bundles. Oberwolfach Reports. 2020;16(2):1357-1417. doi:10.4171/owr/2019/23
apa: Anderson, L., Hausel, T., Mazzeo, R., & Schaposnik, L. (2020). Geometry
and physics of Higgs bundles. Oberwolfach Reports. European Mathematical
Society. https://doi.org/10.4171/owr/2019/23
chicago: Anderson, Lara, Tamás Hausel, Rafe Mazzeo, and Laura Schaposnik. “Geometry
and Physics of Higgs Bundles.” Oberwolfach Reports. European Mathematical
Society, 2020. https://doi.org/10.4171/owr/2019/23.
ieee: L. Anderson, T. Hausel, R. Mazzeo, and L. Schaposnik, “Geometry and physics
of Higgs bundles,” Oberwolfach Reports, vol. 16, no. 2. European Mathematical
Society, pp. 1357–1417, 2020.
ista: Anderson L, Hausel T, Mazzeo R, Schaposnik L. 2020. Geometry and physics of
Higgs bundles. Oberwolfach Reports. 16(2), 1357–1417.
mla: Anderson, Lara, et al. “Geometry and Physics of Higgs Bundles.” Oberwolfach
Reports, vol. 16, no. 2, European Mathematical Society, 2020, pp. 1357–417,
doi:10.4171/owr/2019/23.
short: L. Anderson, T. Hausel, R. Mazzeo, L. Schaposnik, Oberwolfach Reports 16
(2020) 1357–1417.
date_created: 2024-03-04T11:36:31Z
date_published: 2020-06-04T00:00:00Z
date_updated: 2024-03-11T09:20:34Z
day: '04'
department:
- _id: TaHa
doi: 10.4171/owr/2019/23
intvolume: ' 16'
issue: '2'
keyword:
- Organic Chemistry
- Biochemistry
language:
- iso: eng
month: '06'
oa_version: None
page: 1357-1417
publication: Oberwolfach Reports
publication_identifier:
issn:
- 1660-8933
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
status: public
title: Geometry and physics of Higgs bundles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2020'
...
---
_id: '441'
article_processing_charge: No
article_type: original
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Kalinin N, Shkolnikov M. Tropical formulae for summation over a part of SL(2,Z).
European Journal of Mathematics. 2019;5(3):909–928. doi:10.1007/s40879-018-0218-0
apa: Kalinin, N., & Shkolnikov, M. (2019). Tropical formulae for summation over
a part of SL(2,Z). European Journal of Mathematics. Springer Nature. https://doi.org/10.1007/s40879-018-0218-0
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation
over a Part of SL(2,Z).” European Journal of Mathematics. Springer Nature,
2019. https://doi.org/10.1007/s40879-018-0218-0.
ieee: N. Kalinin and M. Shkolnikov, “Tropical formulae for summation over a part
of SL(2,Z),” European Journal of Mathematics, vol. 5, no. 3. Springer Nature,
pp. 909–928, 2019.
ista: Kalinin N, Shkolnikov M. 2019. Tropical formulae for summation over a part
of SL(2,Z). European Journal of Mathematics. 5(3), 909–928.
mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Tropical Formulae for Summation over
a Part of SL(2,Z).” European Journal of Mathematics, vol. 5, no. 3, Springer
Nature, 2019, pp. 909–928, doi:10.1007/s40879-018-0218-0.
short: N. Kalinin, M. Shkolnikov, European Journal of Mathematics 5 (2019) 909–928.
date_created: 2018-12-11T11:46:29Z
date_published: 2019-09-15T00:00:00Z
date_updated: 2021-01-12T07:56:46Z
day: '15'
department:
- _id: TaHa
doi: 10.1007/s40879-018-0218-0
ec_funded: 1
external_id:
arxiv:
- '1711.02089'
intvolume: ' 5'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1711.02089
month: '09'
oa: 1
oa_version: Preprint
page: 909–928
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: European Journal of Mathematics
publication_identifier:
eissn:
- 2199-6768
issn:
- 2199-675X
publication_status: published
publisher: Springer Nature
publist_id: '7382'
quality_controlled: '1'
scopus_import: 1
status: public
title: Tropical formulae for summation over a part of SL(2,Z)
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 5
year: '2019'
...
---
_id: '439'
abstract:
- lang: eng
text: "We count points over a finite field on wild character varieties,of Riemann
surfaces for singularities with regular semisimple leading term. The new feature
in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras.
Our result leads to the conjecture that the mixed Hodge polynomials of these character
varieties agree with previously conjectured perverse Hodge polynomials of certain
twisted parabolic Higgs moduli spaces, indicating the\r\npossibility of a P =
W conjecture for a suitable wild Hitchin system."
article_processing_charge: No
article_type: original
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Martin
full_name: Mereb, Martin
id: 43D735EE-F248-11E8-B48F-1D18A9856A87
last_name: Mereb
- first_name: Michael
full_name: Wong, Michael
last_name: Wong
citation:
ama: Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character
varieties. Journal of the European Mathematical Society. 2019;21(10):2995-3052.
doi:10.4171/JEMS/896
apa: Hausel, T., Mereb, M., & Wong, M. (2019). Arithmetic and representation
theory of wild character varieties. Journal of the European Mathematical Society.
European Mathematical Society. https://doi.org/10.4171/JEMS/896
chicago: Hausel, Tamás, Martin Mereb, and Michael Wong. “Arithmetic and Representation
Theory of Wild Character Varieties.” Journal of the European Mathematical Society.
European Mathematical Society, 2019. https://doi.org/10.4171/JEMS/896.
ieee: T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of
wild character varieties,” Journal of the European Mathematical Society,
vol. 21, no. 10. European Mathematical Society, pp. 2995–3052, 2019.
ista: Hausel T, Mereb M, Wong M. 2019. Arithmetic and representation theory of wild
character varieties. Journal of the European Mathematical Society. 21(10), 2995–3052.
mla: Hausel, Tamás, et al. “Arithmetic and Representation Theory of Wild Character
Varieties.” Journal of the European Mathematical Society, vol. 21, no.
10, European Mathematical Society, 2019, pp. 2995–3052, doi:10.4171/JEMS/896.
short: T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society
21 (2019) 2995–3052.
date_created: 2018-12-11T11:46:29Z
date_published: 2019-10-01T00:00:00Z
date_updated: 2023-08-24T14:24:49Z
day: '01'
department:
- _id: TaHa
doi: 10.4171/JEMS/896
ec_funded: 1
external_id:
arxiv:
- '1604.03382'
isi:
- '000480413600002'
intvolume: ' 21'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1604.03382
month: '10'
oa: 1
oa_version: Preprint
page: 2995-3052
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Journal of the European Mathematical Society
publication_identifier:
eissn:
- 1435-9855
publication_status: published
publisher: European Mathematical Society
publist_id: '7384'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and representation theory of wild character varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 21
year: '2019'
...
---
_id: '6986'
abstract:
- lang: eng
text: 'Li-Nadler proposed a conjecture about traces of Hecke categories, which implies
the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler
in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds
in the natural generality of reflection groups in Euclidean or hyperbolic space.
As a corollary, we give an expression of the centralizer of a finite order element
in a reflection group using homotopy theory. '
article_processing_charge: No
article_type: original
author:
- first_name: Penghui
full_name: Li, Penghui
id: 42A24CCC-F248-11E8-B48F-1D18A9856A87
last_name: Li
citation:
ama: Li P. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 2019;147(11):4597-4604. doi:10.1090/proc/14586
apa: Li, P. (2019). A colimit of traces of reflection groups. Proceedings of
the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14586
chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings
of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14586.
ieee: P. Li, “A colimit of traces of reflection groups,” Proceedings of the American
Mathematical Society, vol. 147, no. 11. AMS, pp. 4597–4604, 2019.
ista: Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 147(11), 4597–4604.
mla: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of
the American Mathematical Society, vol. 147, no. 11, AMS, 2019, pp. 4597–604,
doi:10.1090/proc/14586.
short: P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604.
date_created: 2019-11-04T16:10:50Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-09-05T12:22:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1090/proc/14586
ec_funded: 1
external_id:
arxiv:
- '1810.07039'
isi:
- '000488621700004'
intvolume: ' 147'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.07039
month: '11'
oa: 1
oa_version: Preprint
page: 4597-4604
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: A colimit of traces of reflection groups
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 147
year: '2019'
...
---
_id: '196'
abstract:
- lang: eng
text: 'The abelian sandpile serves as a model to study self-organized criticality,
a phenomenon occurring in biological, physical and social processes. The identity
of the abelian group is a fractal composed of self-similar patches, and its limit
is subject of extensive collaborative research. Here, we analyze the evolution
of the sandpile identity under harmonic fields of different orders. We show that
this evolution corresponds to periodic cycles through the abelian group characterized
by the smooth transformation and apparent conservation of the patches constituting
the identity. The dynamics induced by second and third order harmonics resemble
smooth stretchings, respectively translations, of the identity, while the ones
induced by fourth order harmonics resemble magnifications and rotations. Starting
with order three, the dynamics pass through extended regions of seemingly random
configurations which spontaneously reassemble into accentuated patterns. We show
that the space of harmonic functions projects to the extended analogue of the
sandpile group, thus providing a set of universal coordinates identifying configurations
between different domains. Since the original sandpile group is a subgroup of
the extended one, this directly implies that it admits a natural renormalization.
Furthermore, we show that the harmonic fields can be induced by simple Markov
processes, and that the corresponding stochastic dynamics show remarkable robustness
over hundreds of periods. Finally, we encode information into seemingly random
configurations, and decode this information with an algorithm requiring minimal
prior knowledge. Our results suggest that harmonic fields might split the sandpile
group into sub-sets showing different critical coefficients, and that it might
be possible to extend the fractal structure of the identity beyond the boundaries
of its domain. '
acknowledgement: "M.L. is grateful to the members of the C Guet and G Tkacik groups
for valuable comments and support. M.S. is grateful to Nikita Kalinin for inspiring
communications.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Moritz
full_name: Lang, Moritz
id: 29E0800A-F248-11E8-B48F-1D18A9856A87
last_name: Lang
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Lang M, Shkolnikov M. Harmonic dynamics of the Abelian sandpile. Proceedings
of the National Academy of Sciences. 2019;116(8):2821-2830. doi:10.1073/pnas.1812015116
apa: Lang, M., & Shkolnikov, M. (2019). Harmonic dynamics of the Abelian sandpile.
Proceedings of the National Academy of Sciences. National Academy of Sciences.
https://doi.org/10.1073/pnas.1812015116
chicago: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian
Sandpile.” Proceedings of the National Academy of Sciences. National Academy
of Sciences, 2019. https://doi.org/10.1073/pnas.1812015116.
ieee: M. Lang and M. Shkolnikov, “Harmonic dynamics of the Abelian sandpile,” Proceedings
of the National Academy of Sciences, vol. 116, no. 8. National Academy of
Sciences, pp. 2821–2830, 2019.
ista: Lang M, Shkolnikov M. 2019. Harmonic dynamics of the Abelian sandpile. Proceedings
of the National Academy of Sciences. 116(8), 2821–2830.
mla: Lang, Moritz, and Mikhail Shkolnikov. “Harmonic Dynamics of the Abelian Sandpile.”
Proceedings of the National Academy of Sciences, vol. 116, no. 8, National
Academy of Sciences, 2019, pp. 2821–30, doi:10.1073/pnas.1812015116.
short: M. Lang, M. Shkolnikov, Proceedings of the National Academy of Sciences 116
(2019) 2821–2830.
date_created: 2018-12-11T11:45:08Z
date_published: 2019-02-19T00:00:00Z
date_updated: 2023-09-11T14:09:34Z
day: '19'
department:
- _id: CaGu
- _id: GaTk
- _id: TaHa
doi: 10.1073/pnas.1812015116
external_id:
arxiv:
- '1806.10823'
isi:
- '000459074400013'
pmid:
- ' 30728300'
intvolume: ' 116'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1073/pnas.1812015116
month: '02'
oa: 1
oa_version: Published Version
page: 2821-2830
pmid: 1
publication: Proceedings of the National Academy of Sciences
publication_identifier:
eissn:
- 1091-6490
publication_status: published
publisher: National Academy of Sciences
quality_controlled: '1'
related_material:
link:
- description: News on IST Webpage
relation: press_release
url: https://ist.ac.at/en/news/famous-sandpile-model-shown-to-move-like-a-traveling-sand-dune/
scopus_import: '1'
status: public
title: Harmonic dynamics of the Abelian sandpile
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 116
year: '2019'
...
---
_id: '5'
abstract:
- lang: eng
text: In this paper, we introduce a quantum version of the wonderful compactification
of a group as a certain noncommutative projective scheme. Our approach stems from
the fact that the wonderful compactification encodes the asymptotics of matrix
coefficients, and from its realization as a GIT quotient of the Vinberg semigroup.
In order to define the wonderful compactification for a quantum group, we adopt
a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key
to our construction is a quantum version of the Vinberg semigroup, which we define
as a q-deformation of a certain Rees algebra, compatible with a standard Poisson
structure. Furthermore, we discuss quantum analogues of the stratification of
the wonderful compactification by orbits for a certain group action, and provide
explicit computations in the case of SL2.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Iordan V
full_name: Ganev, Iordan V
id: 447491B8-F248-11E8-B48F-1D18A9856A87
last_name: Ganev
citation:
ama: Ganev IV. The wonderful compactification for quantum groups. Journal of
the London Mathematical Society. 2019;99(3):778-806. doi:10.1112/jlms.12193
apa: Ganev, I. V. (2019). The wonderful compactification for quantum groups. Journal
of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12193
chicago: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal
of the London Mathematical Society. Wiley, 2019. https://doi.org/10.1112/jlms.12193.
ieee: I. V. Ganev, “The wonderful compactification for quantum groups,” Journal
of the London Mathematical Society, vol. 99, no. 3. Wiley, pp. 778–806, 2019.
ista: Ganev IV. 2019. The wonderful compactification for quantum groups. Journal
of the London Mathematical Society. 99(3), 778–806.
mla: Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” Journal
of the London Mathematical Society, vol. 99, no. 3, Wiley, 2019, pp. 778–806,
doi:10.1112/jlms.12193.
short: I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806.
date_created: 2018-12-11T11:44:06Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-19T10:13:08Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1112/jlms.12193
external_id:
isi:
- '000470025900008'
file:
- access_level: open_access
checksum: 1be56239b2cd740a0e9a084f773c22f6
content_type: application/pdf
creator: kschuh
date_created: 2020-01-07T13:31:53Z
date_updated: 2020-07-14T12:46:35Z
file_id: '7238'
file_name: 2019_Wiley_Ganev.pdf
file_size: 431754
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 99'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 778-806
publication: Journal of the London Mathematical Society
publication_status: published
publisher: Wiley
publist_id: '8052'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The wonderful compactification for quantum groups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 99
year: '2019'
...
---
_id: '7436'
abstract:
- lang: eng
text: 'For an ordinary K3 surface over an algebraically closed field of positive
characteristic we show that every automorphism lifts to characteristic zero. Moreover,
we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one
correspondence with the Fourier-Mukai partners of the geometric generic fiber
of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai
partners of the K3 surfaces with Picard rank two and with discriminant equal to
minus of a prime number, in terms of the class number of the prime, holds over
a field of positive characteristic as well. We show that the image of the derived
autoequivalence group of a K3 surface of finite height in the group of isometries
of its crystalline cohomology has index at least two. Moreover, we provide a conditional
upper bound on the kernel of this natural cohomological descent map. Further,
we give an extended remark in the appendix on the possibility of an F-crystal
structure on the crystalline cohomology of a K3 surface over an algebraically
closed field of positive characteristic and show that the naive F-crystal structure
fails in being compatible with inner product. '
article_processing_charge: No
article_type: original
author:
- first_name: Tanya K
full_name: Srivastava, Tanya K
id: 4D046628-F248-11E8-B48F-1D18A9856A87
last_name: Srivastava
citation:
ama: Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 2019;24:1135-1177. doi:10.25537/dm.2019v24.1135-1177
apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive
characteristic. Documenta Mathematica. EMS Press. https://doi.org/10.25537/dm.2019v24.1135-1177
chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive
Characteristic.” Documenta Mathematica. EMS Press, 2019. https://doi.org/10.25537/dm.2019v24.1135-1177.
ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,”
Documenta Mathematica, vol. 24. EMS Press, pp. 1135–1177, 2019.
ista: Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic.
Documenta Mathematica. 24, 1135–1177.
mla: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.”
Documenta Mathematica, vol. 24, EMS Press, 2019, pp. 1135–77, doi:10.25537/dm.2019v24.1135-1177.
short: T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.
date_created: 2020-02-02T23:01:06Z
date_published: 2019-05-20T00:00:00Z
date_updated: 2023-10-17T07:42:21Z
day: '20'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.25537/dm.2019v24.1135-1177
external_id:
arxiv:
- '1809.08970'
isi:
- '000517806400019'
file:
- access_level: open_access
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creator: dernst
date_created: 2020-02-03T06:26:12Z
date_updated: 2020-07-14T12:47:58Z
file_id: '7438'
file_name: 2019_DocumMath_Srivastava.pdf
file_size: 469730
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has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1135-1177
publication: Documenta Mathematica
publication_identifier:
eissn:
- 1431-0643
issn:
- 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On derived equivalences of k3 surfaces in positive characteristic
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2019'
...
---
_id: '61'
abstract:
- lang: eng
text: 'We prove that there is no strongly regular graph (SRG) with parameters (460;
153; 32; 60). The proof is based on a recent lower bound on the number of 4-cliques
in a SRG and some applications of Euclidean representation of SRGs. '
article_processing_charge: No
author:
- first_name: Andriy
full_name: Bondarenko, Andriy
last_name: Bondarenko
- first_name: Anton
full_name: Mellit, Anton
id: 388D3134-F248-11E8-B48F-1D18A9856A87
last_name: Mellit
- first_name: Andriy
full_name: Prymak, Andriy
last_name: Prymak
- first_name: Danylo
full_name: Radchenko, Danylo
last_name: Radchenko
- first_name: Maryna
full_name: Viazovska, Maryna
last_name: Viazovska
citation:
ama: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. There is no strongly
regular graph with parameters (460; 153; 32; 60). In: Contemporary Computational
Mathematics. Springer; 2018:131-134. doi:10.1007/978-3-319-72456-0_7'
apa: Bondarenko, A., Mellit, A., Prymak, A., Radchenko, D., & Viazovska, M.
(2018). There is no strongly regular graph with parameters (460; 153; 32; 60).
In Contemporary Computational Mathematics (pp. 131–134). Springer. https://doi.org/10.1007/978-3-319-72456-0_7
chicago: Bondarenko, Andriy, Anton Mellit, Andriy Prymak, Danylo Radchenko, and
Maryna Viazovska. “There Is No Strongly Regular Graph with Parameters (460; 153;
32; 60).” In Contemporary Computational Mathematics, 131–34. Springer,
2018. https://doi.org/10.1007/978-3-319-72456-0_7.
ieee: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, and M. Viazovska, “There
is no strongly regular graph with parameters (460; 153; 32; 60),” in Contemporary
Computational Mathematics, Springer, 2018, pp. 131–134.
ista: 'Bondarenko A, Mellit A, Prymak A, Radchenko D, Viazovska M. 2018.There is
no strongly regular graph with parameters (460; 153; 32; 60). In: Contemporary
Computational Mathematics. , 131–134.'
mla: Bondarenko, Andriy, et al. “There Is No Strongly Regular Graph with Parameters
(460; 153; 32; 60).” Contemporary Computational Mathematics, Springer,
2018, pp. 131–34, doi:10.1007/978-3-319-72456-0_7.
short: A. Bondarenko, A. Mellit, A. Prymak, D. Radchenko, M. Viazovska, in:, Contemporary
Computational Mathematics, Springer, 2018, pp. 131–134.
date_created: 2018-12-11T11:44:25Z
date_published: 2018-05-23T00:00:00Z
date_updated: 2021-01-12T08:06:06Z
day: '23'
department:
- _id: TaHa
doi: 10.1007/978-3-319-72456-0_7
extern: '1'
external_id:
arxiv:
- '1509.06286'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1509.06286
month: '05'
oa: 1
oa_version: Preprint
page: 131 - 134
publication: Contemporary Computational Mathematics
publication_status: published
publisher: Springer
publist_id: '7993'
quality_controlled: '1'
status: public
title: There is no strongly regular graph with parameters (460; 153; 32; 60)
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '6525'
abstract:
- lang: eng
text: This chapter finds an agreement of equivariant indices of semi-classical homomorphisms
between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface.
On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs
bundles, whose mirror was proposed by Hitchin to be certain even exterior powers
of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present.
The agreement arises from a mysterious functional equation. This gives strong
computational evidence for Hitchin’s proposal.
author:
- first_name: Tamás
full_name: Hausel, Tamás
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Anton
full_name: Mellit, Anton
id: 388D3134-F248-11E8-B48F-1D18A9856A87
last_name: Mellit
- first_name: Du
full_name: Pei, Du
last_name: Pei
citation:
ama: 'Hausel T, Mellit A, Pei D. Mirror symmetry with branes by equivariant verlinde
formulas. In: Geometry and Physics: Volume I. Oxford University Press;
2018:189-218. doi:10.1093/oso/9780198802013.003.0009'
apa: 'Hausel, T., Mellit, A., & Pei, D. (2018). Mirror symmetry with branes
by equivariant verlinde formulas. In Geometry and Physics: Volume I (pp.
189–218). Oxford University Press. https://doi.org/10.1093/oso/9780198802013.003.0009'
chicago: 'Hausel, Tamás, Anton Mellit, and Du Pei. “Mirror Symmetry with Branes
by Equivariant Verlinde Formulas.” In Geometry and Physics: Volume I, 189–218.
Oxford University Press, 2018. https://doi.org/10.1093/oso/9780198802013.003.0009.'
ieee: 'T. Hausel, A. Mellit, and D. Pei, “Mirror symmetry with branes by equivariant
verlinde formulas,” in Geometry and Physics: Volume I, Oxford University
Press, 2018, pp. 189–218.'
ista: 'Hausel T, Mellit A, Pei D. 2018.Mirror symmetry with branes by equivariant
verlinde formulas. In: Geometry and Physics: Volume I. , 189–218.'
mla: 'Hausel, Tamás, et al. “Mirror Symmetry with Branes by Equivariant Verlinde
Formulas.” Geometry and Physics: Volume I, Oxford University Press, 2018,
pp. 189–218, doi:10.1093/oso/9780198802013.003.0009.'
short: 'T. Hausel, A. Mellit, D. Pei, in:, Geometry and Physics: Volume I, Oxford
University Press, 2018, pp. 189–218.'
date_created: 2019-06-06T12:42:01Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2021-01-12T08:07:52Z
day: '01'
department:
- _id: TaHa
doi: 10.1093/oso/9780198802013.003.0009
language:
- iso: eng
month: '01'
oa_version: None
page: 189-218
publication: 'Geometry and Physics: Volume I'
publication_identifier:
isbn:
- '9780198802013'
- '9780191840500'
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: 1
status: public
title: Mirror symmetry with branes by equivariant verlinde formulas
type: book_chapter
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '303'
abstract:
- lang: eng
text: The theory of tropical series, that we develop here, firstly appeared in the
study of the growth of pluriharmonic functions. Motivated by waves in sandpile
models we introduce a dynamic on the set of tropical series, and it is experimentally
observed that this dynamic obeys a power law. So, this paper serves as a compilation
of results we need for other articles and also introduces several objects interesting
by themselves.
acknowledgement: The first author, Nikita Kalinin, is funded by SNCF PostDoc.Mobility
grant 168647. Support from the Basic Research Program of the National Research University
Higher School of Economics is gratefully acknowledged. The second author, Mikhail
Shkolnikov, is supported in part by the grant 159240 of the Swiss National Science
Foundation as well as by the National Center of Competence in Research SwissMAP
of the Swiss National Science Foundation.
article_processing_charge: No
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
citation:
ama: Kalinin N, Shkolnikov M. Introduction to tropical series and wave dynamic on
them. Discrete and Continuous Dynamical Systems- Series A. 2018;38(6):2827-2849.
doi:10.3934/dcds.2018120
apa: Kalinin, N., & Shkolnikov, M. (2018). Introduction to tropical series and
wave dynamic on them. Discrete and Continuous Dynamical Systems- Series A.
AIMS. https://doi.org/10.3934/dcds.2018120
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series
and Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series
A. AIMS, 2018. https://doi.org/10.3934/dcds.2018120.
ieee: N. Kalinin and M. Shkolnikov, “Introduction to tropical series and wave dynamic
on them,” Discrete and Continuous Dynamical Systems- Series A, vol. 38,
no. 6. AIMS, pp. 2827–2849, 2018.
ista: Kalinin N, Shkolnikov M. 2018. Introduction to tropical series and wave dynamic
on them. Discrete and Continuous Dynamical Systems- Series A. 38(6), 2827–2849.
mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Introduction to Tropical Series and
Wave Dynamic on Them.” Discrete and Continuous Dynamical Systems- Series A,
vol. 38, no. 6, AIMS, 2018, pp. 2827–49, doi:10.3934/dcds.2018120.
short: N. Kalinin, M. Shkolnikov, Discrete and Continuous Dynamical Systems- Series
A 38 (2018) 2827–2849.
date_created: 2018-12-11T11:45:43Z
date_published: 2018-06-01T00:00:00Z
date_updated: 2023-09-12T07:45:37Z
day: '01'
department:
- _id: TaHa
doi: 10.3934/dcds.2018120
external_id:
arxiv:
- '1706.03062'
isi:
- '000438818400007'
intvolume: ' 38'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.03062
month: '06'
oa: 1
oa_version: Submitted Version
page: 2827 - 2849
publication: Discrete and Continuous Dynamical Systems- Series A
publication_status: published
publisher: AIMS
publist_id: '7576'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Introduction to tropical series and wave dynamic on them
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 38
year: '2018'
...
---
_id: '322'
abstract:
- lang: eng
text: We construct quantizations of multiplicative hypertoric varieties using an
algebra of q-difference operators on affine space, where q is a root of unity
in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the
multiplicative hypertoric variety and admits an explicit finite étale splitting.
The global sections of this Azumaya algebra is a hypertoric quantum group, and
we prove a localization theorem. We introduce a general framework of Frobenius
quantum moment maps and their Hamiltonian reductions; our results shed light on
an instance of this framework.
acknowledgement: "National Science Foundation: Graduate Research Fellowship and grant
No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces”
No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project
and providing guidance throughout, particularly for the formulation of Frobenius
quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special
thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and
constant encouragement, and for suggesting the term ‘hypertoric quantum group.’
Many results appearing in the current paper were proven independently by Nicholas
Cooney; the author is grateful to Nicholas for sharing his insight on various topics,
including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating
the definition of multiplicative hypertoric varieties, as well as the content of
Remark 2.14. The author also benefited immensely from the close reading and detailed
comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi
Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n"
article_processing_charge: No
author:
- first_name: Iordan V
full_name: Ganev, Iordan V
id: 447491B8-F248-11E8-B48F-1D18A9856A87
last_name: Ganev
citation:
ama: Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of
unity. Journal of Algebra. 2018;506:92-128. doi:10.1016/j.jalgebra.2018.03.015
apa: Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at
a root of unity. Journal of Algebra. World Scientific Publishing. https://doi.org/10.1016/j.jalgebra.2018.03.015
chicago: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties
at a Root of Unity.” Journal of Algebra. World Scientific Publishing, 2018.
https://doi.org/10.1016/j.jalgebra.2018.03.015.
ieee: I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root
of unity,” Journal of Algebra, vol. 506. World Scientific Publishing, pp.
92–128, 2018.
ista: Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a
root of unity. Journal of Algebra. 506, 92–128.
mla: Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a
Root of Unity.” Journal of Algebra, vol. 506, World Scientific Publishing,
2018, pp. 92–128, doi:10.1016/j.jalgebra.2018.03.015.
short: I.V. Ganev, Journal of Algebra 506 (2018) 92–128.
date_created: 2018-12-11T11:45:49Z
date_published: 2018-07-15T00:00:00Z
date_updated: 2023-09-15T12:08:38Z
day: '15'
department:
- _id: TaHa
doi: 10.1016/j.jalgebra.2018.03.015
ec_funded: 1
external_id:
arxiv:
- '1412.7211'
isi:
- '000433270600005'
intvolume: ' 506'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1412.7211
month: '07'
oa: 1
oa_version: Preprint
page: 92 - 128
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Journal of Algebra
publication_status: published
publisher: World Scientific Publishing
publist_id: '7543'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantizations of multiplicative hypertoric varieties at a root of unity
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 506
year: '2018'
...
---
_id: '64'
abstract:
- lang: eng
text: Tropical geometry, an established field in pure mathematics, is a place where
string theory, mirror symmetry, computational algebra, auction theory, and so
forth meet and influence one another. In this paper, we report on our discovery
of a tropical model with self-organized criticality (SOC) behavior. Our model
is continuous, in contrast to all known models of SOC, and is a certain scaling
limit of the sandpile model, the first and archetypical model of SOC. We describe
how our model is related to pattern formation and proportional growth phenomena
and discuss the dichotomy between continuous and discrete models in several contexts.
Our aim in this context is to present an idealized tropical toy model (cf. Turing
reaction-diffusion model), requiring further investigation.
article_processing_charge: No
article_type: original
author:
- first_name: Nikita
full_name: Kalinin, Nikita
last_name: Kalinin
- first_name: Aldo
full_name: Guzmán Sáenz, Aldo
last_name: Guzmán Sáenz
- first_name: Y
full_name: Prieto, Y
last_name: Prieto
- first_name: Mikhail
full_name: Shkolnikov, Mikhail
id: 35084A62-F248-11E8-B48F-1D18A9856A87
last_name: Shkolnikov
orcid: 0000-0002-4310-178X
- first_name: V
full_name: Kalinina, V
last_name: Kalinina
- first_name: Ernesto
full_name: Lupercio, Ernesto
last_name: Lupercio
citation:
ama: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E.
Self-organized criticality and pattern emergence through the lens of tropical
geometry. PNAS: Proceedings of the National Academy of Sciences of the United
States of America. 2018;115(35):E8135-E8142. doi:10.1073/pnas.1805847115'
apa: 'Kalinin, N., Guzmán Sáenz, A., Prieto, Y., Shkolnikov, M., Kalinina, V., &
Lupercio, E. (2018). Self-organized criticality and pattern emergence through
the lens of tropical geometry. PNAS: Proceedings of the National Academy of
Sciences of the United States of America. National Academy of Sciences. https://doi.org/10.1073/pnas.1805847115'
chicago: 'Kalinin, Nikita, Aldo Guzmán Sáenz, Y Prieto, Mikhail Shkolnikov, V Kalinina,
and Ernesto Lupercio. “Self-Organized Criticality and Pattern Emergence through
the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy of
Sciences of the United States of America. National Academy of Sciences, 2018.
https://doi.org/10.1073/pnas.1805847115.'
ieee: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, and E.
Lupercio, “Self-organized criticality and pattern emergence through the lens of
tropical geometry,” PNAS: Proceedings of the National Academy of Sciences of
the United States of America, vol. 115, no. 35. National Academy of Sciences,
pp. E8135–E8142, 2018.'
ista: 'Kalinin N, Guzmán Sáenz A, Prieto Y, Shkolnikov M, Kalinina V, Lupercio E.
2018. Self-organized criticality and pattern emergence through the lens of tropical
geometry. PNAS: Proceedings of the National Academy of Sciences of the United
States of America. 115(35), E8135–E8142.'
mla: 'Kalinin, Nikita, et al. “Self-Organized Criticality and Pattern Emergence
through the Lens of Tropical Geometry.” PNAS: Proceedings of the National Academy
of Sciences of the United States of America, vol. 115, no. 35, National Academy
of Sciences, 2018, pp. E8135–42, doi:10.1073/pnas.1805847115.'
short: 'N. Kalinin, A. Guzmán Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio,
PNAS: Proceedings of the National Academy of Sciences of the United States of
America 115 (2018) E8135–E8142.'
date_created: 2018-12-11T11:44:26Z
date_published: 2018-08-28T00:00:00Z
date_updated: 2023-09-18T08:41:16Z
day: '28'
department:
- _id: TaHa
doi: 10.1073/pnas.1805847115
ec_funded: 1
external_id:
arxiv:
- '1806.09153'
isi:
- '000442861600009'
intvolume: ' 115'
isi: 1
issue: '35'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.09153
month: '08'
oa: 1
oa_version: Preprint
page: E8135 - E8142
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: 'PNAS: Proceedings of the National Academy of Sciences of the United
States of America'
publication_identifier:
issn:
- '00278424'
publication_status: published
publisher: National Academy of Sciences
publist_id: '7990'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Self-organized criticality and pattern emergence through the lens of tropical
geometry
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 115
year: '2018'
...
---
_id: '5999'
abstract:
- lang: eng
text: "We introduce for each quiver Q and each algebraic oriented cohomology theory
A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli
of representations of the preprojective algebra of Q. This generalizes the K-theoretic
Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is
the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's
reformulated conjecture on modular representations of algebraic groups.\r\nWe
construct an action of the preprojective CoHA on the A-homology of Nakajima quiver
varieties. We compare this with the action of the Borel subalgebra of Yangian
when A is the intersection theory. We also give a shuffle algebra description
of this CoHA in terms of the underlying formal group law of A. As applications,
we obtain a shuffle description of the Yangian. "
article_processing_charge: No
author:
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 2018;116(5):1029-1074.
doi:10.1112/plms.12111
apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective
algebra. Proceedings of the London Mathematical Society. Oxford University
Press. https://doi.org/10.1112/plms.12111
chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society. Oxford University
Press, 2018. https://doi.org/10.1112/plms.12111.
ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,”
Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford
University Press, pp. 1029–1074, 2018.
ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 116(5), 1029–1074.
mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society, vol. 116, no.
5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111.
short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018)
1029–1074.
date_created: 2019-02-14T13:14:22Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2023-09-19T14:37:19Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/plms.12111
external_id:
arxiv:
- '1407.7994'
isi:
- '000431506400001'
intvolume: ' 116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1407.7994
month: '05'
oa: 1
oa_version: Preprint
page: 1029-1074
publication: Proceedings of the London Mathematical Society
publication_identifier:
issn:
- 0024-6115
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The cohomological Hall algebra of a preprojective algebra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 116
year: '2018'
...
---
_id: '687'
abstract:
- lang: eng
text: Pursuing the similarity between the Kontsevich-Soibelman construction of the
cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of
canonical bases for quantum enveloping algebras, and the similarity between the
integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem
for quantum enveloping algebras, we build a coproduct on the CoHA associated to
a quiver with potential. We also prove a cohomological dimensional reduction theorem,
further linking a special class of CoHAs with Yangians, and explaining how to
connect the study of character varieties with the study of CoHAs.
author:
- first_name: Ben
full_name: Davison, Ben
id: 4634AB1E-F248-11E8-B48F-1D18A9856A87
last_name: Davison
orcid: 0000-0002-8944-4390
citation:
ama: Davison B. The critical CoHA of a quiver with potential. Quarterly Journal
of Mathematics. 2017;68(2):635-703. doi:10.1093/qmath/haw053
apa: Davison, B. (2017). The critical CoHA of a quiver with potential. Quarterly
Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haw053
chicago: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly
Journal of Mathematics. Oxford University Press, 2017. https://doi.org/10.1093/qmath/haw053.
ieee: B. Davison, “The critical CoHA of a quiver with potential,” Quarterly Journal
of Mathematics, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017.
ista: Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal
of Mathematics. 68(2), 635–703.
mla: Davison, Ben. “The Critical CoHA of a Quiver with Potential.” Quarterly
Journal of Mathematics, vol. 68, no. 2, Oxford University Press, 2017, pp.
635–703, doi:10.1093/qmath/haw053.
short: B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.
date_created: 2018-12-11T11:47:55Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2021-01-12T08:09:24Z
day: '01'
department:
- _id: TaHa
doi: 10.1093/qmath/haw053
ec_funded: 1
intvolume: ' 68'
issue: '2'
language:
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url: https://arxiv.org/abs/1311.7172
month: '06'
oa: 1
oa_version: Submitted Version
page: 635 - 703
project:
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call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Quarterly Journal of Mathematics
publication_identifier:
issn:
- '00335606'
publication_status: published
publisher: Oxford University Press
publist_id: '7022'
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scopus_import: 1
status: public
title: The critical CoHA of a quiver with potential
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 68
year: '2017'
...