---
_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for explaining their work but also for sharing some unpublished results with us.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
arxiv: 1
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: '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
arxiv: 1
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: '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
arxiv: 1
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
orcid: 0000-0001-6889-1418
- 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: 2024-08-07T07:16:52Z
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
arxiv: 1
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: '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
arxiv: 1
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
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creator: dernst
date_created: 2024-01-30T12:56:00Z
date_updated: 2024-01-30T12:56:00Z
file_id: '14910'
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file_size: 651335
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has_accepted_license: '1'
intvolume: ' 127'
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- 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:
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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: '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: '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
arxiv: 1
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
arxiv: 1
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:
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checksum: 8bd0fd9694be894a191857ddf27678f0
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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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file_date_updated: 2022-02-21T11:22:58Z
has_accepted_license: '1'
intvolume: ' 105'
isi: 1
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:
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(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: '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
arxiv: 1
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: '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
arxiv: 1
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: '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
arxiv: 1
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: '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
arxiv: 1
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
arxiv: 1
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
arxiv: 1
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
arxiv: 1
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: '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
arxiv: 1
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: '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: '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
arxiv: 1
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
arxiv: 1
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'
...