---
_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
file_id: '10010'
file_name: 2021_SelectaMath_Koroteev.pdf
file_size: 584648
relation: main_file
success: 1
file_date_updated: 2021-09-13T11:31:34Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
issue: '5'
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'
...