---
_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
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:56:00Z
date_updated: 2024-01-30T12:56:00Z
file_id: '14910'
file_name: 2023_ProcLondonMathSoc_Hausel.pdf
file_size: 651335
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:56:00Z
has_accepted_license: '1'
intvolume: ' 127'
isi: 1
issue: '4'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 958-1027
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 25E6C798-B435-11E9-9278-68D0E5697425
grant_number: '153627'
name: Arithmetic quantization of character and quiver varities
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic and metric aspects of open de Rham spaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 127
year: '2023'
...
---
_id: '9581'
abstract:
- lang: eng
text: "We show that for any \U0001D45B divisible by 3, almost all order- \U0001D45B
\ Steiner triple systems have a perfect matching (also known as a parallel class
or resolution class). In fact, we prove a general upper bound on the number of
perfect matchings in a Steiner triple system and show that almost all Steiner
triple systems essentially attain this maximum. We accomplish this via a general
theorem comparing a uniformly random Steiner triple system to the outcome of the
triangle removal process, which we hope will be useful for other problems. Our
methods can also be adapted to other types of designs; for example, we sketch
a proof of the theorem that almost all Latin squares have transversals."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
citation:
ama: Kwan MA. Almost all Steiner triple systems have perfect matchings. Proceedings
of the London Mathematical Society. 2020;121(6):1468-1495. doi:10.1112/plms.12373
apa: Kwan, M. A. (2020). Almost all Steiner triple systems have perfect matchings.
Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.12373
chicago: Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.”
Proceedings of the London Mathematical Society. Wiley, 2020. https://doi.org/10.1112/plms.12373.
ieee: M. A. Kwan, “Almost all Steiner triple systems have perfect matchings,” Proceedings
of the London Mathematical Society, vol. 121, no. 6. Wiley, pp. 1468–1495,
2020.
ista: Kwan MA. 2020. Almost all Steiner triple systems have perfect matchings. Proceedings
of the London Mathematical Society. 121(6), 1468–1495.
mla: Kwan, Matthew Alan. “Almost All Steiner Triple Systems Have Perfect Matchings.”
Proceedings of the London Mathematical Society, vol. 121, no. 6, Wiley,
2020, pp. 1468–95, doi:10.1112/plms.12373.
short: M.A. Kwan, Proceedings of the London Mathematical Society 121 (2020) 1468–1495.
date_created: 2021-06-22T06:35:16Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2023-02-23T14:01:43Z
day: '01'
doi: 10.1112/plms.12373
extern: '1'
external_id:
arxiv:
- '1611.02246'
intvolume: ' 121'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1611.02246
month: '12'
oa: 1
oa_version: Preprint
page: 1468-1495
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: Almost all Steiner triple systems have perfect matchings
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 121
year: '2020'
...
---
_id: '5999'
abstract:
- lang: eng
text: "We introduce for each quiver Q and each algebraic oriented cohomology theory
A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli
of representations of the preprojective algebra of Q. This generalizes the K-theoretic
Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is
the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's
reformulated conjecture on modular representations of algebraic groups.\r\nWe
construct an action of the preprojective CoHA on the A-homology of Nakajima quiver
varieties. We compare this with the action of the Borel subalgebra of Yangian
when A is the intersection theory. We also give a shuffle algebra description
of this CoHA in terms of the underlying formal group law of A. As applications,
we obtain a shuffle description of the Yangian. "
article_processing_charge: No
arxiv: 1
author:
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 2018;116(5):1029-1074.
doi:10.1112/plms.12111
apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective
algebra. Proceedings of the London Mathematical Society. Oxford University
Press. https://doi.org/10.1112/plms.12111
chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society. Oxford University
Press, 2018. https://doi.org/10.1112/plms.12111.
ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,”
Proceedings of the London Mathematical Society, vol. 116, no. 5. Oxford
University Press, pp. 1029–1074, 2018.
ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 116(5), 1029–1074.
mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” Proceedings of the London Mathematical Society, vol. 116, no.
5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111.
short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018)
1029–1074.
date_created: 2019-02-14T13:14:22Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2023-09-19T14:37:19Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/plms.12111
external_id:
arxiv:
- '1407.7994'
isi:
- '000431506400001'
intvolume: ' 116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1407.7994
month: '05'
oa: 1
oa_version: Preprint
page: 1029-1074
publication: Proceedings of the London Mathematical Society
publication_identifier:
issn:
- 0024-6115
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The cohomological Hall algebra of a preprojective algebra
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 116
year: '2018'
...
---
_id: '270'
abstract:
- lang: eng
text: Given a symmetric variety Y defined over Q and a non-zero polynomial with
integer coefficients, we use techniques from homogeneous dynamics to establish
conditions under which the polynomial can be made r-free for a Zariski dense set
of integral points on Y . We also establish an asymptotic counting formula for
this set. In the special case that Y is a quadric hypersurface, we give explicit
bounds on the size of r by combining the argument with a uniform upper bound for
the density of integral points on general affine quadrics defined over Q.
acknowledgement: While working on this paper the authors were supported by ERC grants
306457 and 239606, respectively.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Alexander
full_name: Gorodnik, Alexander
last_name: Gorodnik
citation:
ama: Browning TD, Gorodnik A. Power-free values of polynomials on symmetric varieties.
Proceedings of the London Mathematical Society. 2017;114(6):1044-1080.
doi:10.1112/plms.12030
apa: Browning, T. D., & Gorodnik, A. (2017). Power-free values of polynomials
on symmetric varieties. Proceedings of the London Mathematical Society.
Wiley. https://doi.org/10.1112/plms.12030
chicago: Browning, Timothy D, and Alexander Gorodnik. “Power-Free Values of Polynomials
on Symmetric Varieties.” Proceedings of the London Mathematical Society.
Wiley, 2017. https://doi.org/10.1112/plms.12030.
ieee: T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric
varieties,” Proceedings of the London Mathematical Society, vol. 114, no.
6. Wiley, pp. 1044–1080, 2017.
ista: Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric
varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080.
mla: Browning, Timothy D., and Alexander Gorodnik. “Power-Free Values of Polynomials
on Symmetric Varieties.” Proceedings of the London Mathematical Society,
vol. 114, no. 6, Wiley, 2017, pp. 1044–80, doi:10.1112/plms.12030.
short: T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society
114 (2017) 1044–1080.
date_created: 2018-12-11T11:45:32Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2024-03-05T11:58:25Z
day: '01'
doi: 10.1112/plms.12030
extern: '1'
external_id:
arxiv:
- '1606.06342'
intvolume: ' 114'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1606.06342
month: '06'
oa: 1
oa_version: Preprint
page: 1044 - 1080
publication: Proceedings of the London Mathematical Society
publication_identifier:
issn:
- 0024-6115
publication_status: published
publisher: Wiley
publist_id: '7632'
quality_controlled: '1'
status: public
title: Power-free values of polynomials on symmetric varieties
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 114
year: '2017'
...