---
_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for explaining their work but also for sharing some unpublished results with us.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:
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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'
...