---
_id: '12427'
abstract:
- lang: eng
text: 'Let k be a number field and X a smooth, geometrically integral quasi-projective
variety over k. For any linear algebraic group G over k and any G-torsor g : Z
→ X, we observe that if the étale-Brauer obstruction is the only one for strong
approximation off a finite set of places S for all twists of Z by elements in
H^1(k, G), then the étale-Brauer obstruction is the only one for strong approximation
off a finite set of places S for X. As an application, we show that any homogeneous
space of the form G/H with G a connected linear algebraic group over k satisfies
strong approximation off the infinite places with étale-Brauer obstruction, under
some compactness assumptions when k is totally real. We also prove more refined
strong approximation results for homogeneous spaces of the form G/H with G semisimple
simply connected and H finite, using the theory of torsors and descent.'
article_processing_charge: No
article_type: original
author:
- first_name: Francesca
full_name: Balestrieri, Francesca
id: 3ACCD756-F248-11E8-B48F-1D18A9856A87
last_name: Balestrieri
citation:
ama: Balestrieri F. Some remarks on strong approximation and applications to homogeneous
spaces of linear algebraic groups. Proceedings of the American Mathematical
Society. 2023;151(3):907-914. doi:10.1090/proc/15239
apa: Balestrieri, F. (2023). Some remarks on strong approximation and applications
to homogeneous spaces of linear algebraic groups. Proceedings of the American
Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15239
chicago: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications
to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American
Mathematical Society. American Mathematical Society, 2023. https://doi.org/10.1090/proc/15239.
ieee: F. Balestrieri, “Some remarks on strong approximation and applications to
homogeneous spaces of linear algebraic groups,” Proceedings of the American
Mathematical Society, vol. 151, no. 3. American Mathematical Society, pp.
907–914, 2023.
ista: Balestrieri F. 2023. Some remarks on strong approximation and applications
to homogeneous spaces of linear algebraic groups. Proceedings of the American
Mathematical Society. 151(3), 907–914.
mla: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications
to Homogeneous Spaces of Linear Algebraic Groups.” Proceedings of the American
Mathematical Society, vol. 151, no. 3, American Mathematical Society, 2023,
pp. 907–14, doi:10.1090/proc/15239.
short: F. Balestrieri, Proceedings of the American Mathematical Society 151 (2023)
907–914.
date_created: 2023-01-29T23:00:58Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-08-01T13:03:32Z
day: '01'
department:
- _id: TiBr
doi: 10.1090/proc/15239
external_id:
isi:
- '000898440000001'
intvolume: ' 151'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.science/hal-03013498/
month: '01'
oa: 1
oa_version: Preprint
page: 907-914
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some remarks on strong approximation and applications to homogeneous spaces
of linear algebraic groups
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 151
year: '2023'
...
---
_id: '13177'
abstract:
- lang: eng
text: In this note we study the eigenvalue growth of infinite graphs with discrete
spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type
inequalities and that the total measure is finite. In this sense, the associated
operators on these graphs display similarities to elliptic operators on bounded
domains in the continuum. Specifically, we prove lower bounds on the eigenvalue
growth and show by examples that corresponding upper bounds cannot be established.
acknowledgement: The second author was supported by the priority program SPP2026 of
the German Research Foundation (DFG). The fourth author was supported by the German
Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the
German Research Foundation (DFG) via RTG 1523/2.
article_processing_charge: No
article_type: original
author:
- first_name: Bobo
full_name: Hua, Bobo
last_name: Hua
- first_name: Matthias
full_name: Keller, Matthias
last_name: Keller
- first_name: Michael
full_name: Schwarz, Michael
last_name: Schwarz
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue
growth on graphs with finite measure. Proceedings of the American Mathematical
Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361
apa: Hua, B., Keller, M., Schwarz, M., & Wirth, M. (2023). Sobolev-type inequalities
and eigenvalue growth on graphs with finite measure. Proceedings of the American
Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/14361
chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type
Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings
of the American Mathematical Society. American Mathematical Society, 2023.
https://doi.org/10.1090/proc/14361.
ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and
eigenvalue growth on graphs with finite measure,” Proceedings of the American
Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp.
3401–3414, 2023.
ista: Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue
growth on graphs with finite measure. Proceedings of the American Mathematical
Society. 151(8), 3401–3414.
mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs
with Finite Measure.” Proceedings of the American Mathematical Society,
vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361.
short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical
Society 151 (2023) 3401–3414.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-11-14T13:07:09Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/proc/14361
external_id:
arxiv:
- '1804.08353'
isi:
- '000988204400001'
intvolume: ' 151'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1804.08353'
month: '08'
oa: 1
oa_version: Preprint
page: 3401-3414
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 151
year: '2023'
...
---
_id: '8773'
abstract:
- lang: eng
text: Let g be a complex semisimple Lie algebra. We give a classification of contravariant
forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We
prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose
dimension is given by the cardinality of the Weyl group of g. We also describe
a procedure for parabolically inducing contravariant forms. As a corollary, we
deduce the existence of the Shapovalov form on a Verma module, and provide a formula
for the dimension of the space of contravariant forms on the degenerate Whittaker
modules M(χ,η) introduced by McDowell.
acknowledgement: "We would like to thank Peter Trapa for useful discussions, and Dragan
Milicic and Arun Ram for valuable feedback on the structure of the paper. The first
author acknowledges the support of the European Unions Horizon 2020 research and
innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411.
The second author is\r\nsupported by the National Science Foundation Award No. 1803059."
article_processing_charge: No
article_type: original
author:
- first_name: Adam
full_name: Brown, Adam
id: 70B7FDF6-608D-11E9-9333-8535E6697425
last_name: Brown
- first_name: Anna
full_name: Romanov, Anna
last_name: Romanov
citation:
ama: Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 2021;149(1):37-52. doi:10.1090/proc/15205
apa: Brown, A., & Romanov, A. (2021). Contravariant forms on Whittaker modules.
Proceedings of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/proc/15205
chicago: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society. American Mathematical
Society, 2021. https://doi.org/10.1090/proc/15205.
ieee: A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings
of the American Mathematical Society, vol. 149, no. 1. American Mathematical
Society, pp. 37–52, 2021.
ista: Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings
of the American Mathematical Society. 149(1), 37–52.
mla: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
Proceedings of the American Mathematical Society, vol. 149, no. 1, American
Mathematical Society, 2021, pp. 37–52, doi:10.1090/proc/15205.
short: A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149
(2021) 37–52.
date_created: 2020-11-19T10:17:40Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:11:47Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/15205
ec_funded: 1
external_id:
arxiv:
- '1910.08286'
isi:
- '000600416300004'
intvolume: ' 149'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.08286
month: '01'
oa: 1
oa_version: Preprint
page: 37-52
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: Contravariant forms on Whittaker modules
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 149
year: '2021'
...
---
_id: '6986'
abstract:
- lang: eng
text: 'Li-Nadler proposed a conjecture about traces of Hecke categories, which implies
the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler
in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds
in the natural generality of reflection groups in Euclidean or hyperbolic space.
As a corollary, we give an expression of the centralizer of a finite order element
in a reflection group using homotopy theory. '
article_processing_charge: No
article_type: original
author:
- first_name: Penghui
full_name: Li, Penghui
id: 42A24CCC-F248-11E8-B48F-1D18A9856A87
last_name: Li
citation:
ama: Li P. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 2019;147(11):4597-4604. doi:10.1090/proc/14586
apa: Li, P. (2019). A colimit of traces of reflection groups. Proceedings of
the American Mathematical Society. AMS. https://doi.org/10.1090/proc/14586
chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings
of the American Mathematical Society. AMS, 2019. https://doi.org/10.1090/proc/14586.
ieee: P. Li, “A colimit of traces of reflection groups,” Proceedings of the American
Mathematical Society, vol. 147, no. 11. AMS, pp. 4597–4604, 2019.
ista: Li P. 2019. A colimit of traces of reflection groups. Proceedings of the American
Mathematical Society. 147(11), 4597–4604.
mla: Li, Penghui. “A Colimit of Traces of Reflection Groups.” Proceedings of
the American Mathematical Society, vol. 147, no. 11, AMS, 2019, pp. 4597–604,
doi:10.1090/proc/14586.
short: P. Li, Proceedings of the American Mathematical Society 147 (2019) 4597–4604.
date_created: 2019-11-04T16:10:50Z
date_published: 2019-11-01T00:00:00Z
date_updated: 2023-09-05T12:22:21Z
day: '01'
department:
- _id: TaHa
doi: 10.1090/proc/14586
ec_funded: 1
external_id:
arxiv:
- '1810.07039'
isi:
- '000488621700004'
intvolume: ' 147'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1810.07039
month: '11'
oa: 1
oa_version: Preprint
page: 4597-4604
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: AMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: A colimit of traces of reflection groups
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 147
year: '2019'
...
---
_id: '8495'
abstract:
- lang: eng
text: 'In this note, we consider the dynamics associated to a perturbation of an
integrable Hamiltonian system in action-angle coordinates in any number of degrees
of freedom and we prove the following result of ``micro-diffusion'''': under generic
assumptions on $ h$ and $ f$, there exists an orbit of the system for which the
drift of its action variables is at least of order $ \sqrt {\varepsilon }$, after
a time of order $ \sqrt {\varepsilon }^{-1}$. The assumptions, which are essentially
minimal, are that there exists a resonant point for $ h$ and that the corresponding
averaged perturbation is non-constant. The conclusions, although very weak when
compared to usual instability phenomena, are also essentially optimal within this
setting.'
article_processing_charge: No
article_type: letter_note
author:
- first_name: Abed
full_name: Bounemoura, Abed
last_name: Bounemoura
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Bounemoura A, Kaloshin V. A note on micro-instability for Hamiltonian systems
close to integrable. Proceedings of the American Mathematical Society.
2015;144(4):1553-1560. doi:10.1090/proc/12796
apa: Bounemoura, A., & Kaloshin, V. (2015). A note on micro-instability for
Hamiltonian systems close to integrable. Proceedings of the American Mathematical
Society. American Mathematical Society. https://doi.org/10.1090/proc/12796
chicago: Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for
Hamiltonian Systems Close to Integrable.” Proceedings of the American Mathematical
Society. American Mathematical Society, 2015. https://doi.org/10.1090/proc/12796.
ieee: A. Bounemoura and V. Kaloshin, “A note on micro-instability for Hamiltonian
systems close to integrable,” Proceedings of the American Mathematical Society,
vol. 144, no. 4. American Mathematical Society, pp. 1553–1560, 2015.
ista: Bounemoura A, Kaloshin V. 2015. A note on micro-instability for Hamiltonian
systems close to integrable. Proceedings of the American Mathematical Society.
144(4), 1553–1560.
mla: Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for Hamiltonian
Systems Close to Integrable.” Proceedings of the American Mathematical Society,
vol. 144, no. 4, American Mathematical Society, 2015, pp. 1553–60, doi:10.1090/proc/12796.
short: A. Bounemoura, V. Kaloshin, Proceedings of the American Mathematical Society
144 (2015) 1553–1560.
date_created: 2020-09-18T10:46:14Z
date_published: 2015-12-21T00:00:00Z
date_updated: 2021-01-12T08:19:40Z
day: '21'
doi: 10.1090/proc/12796
extern: '1'
intvolume: ' 144'
issue: '4'
language:
- iso: eng
month: '12'
oa_version: None
page: 1553-1560
publication: Proceedings of the American Mathematical Society
publication_identifier:
issn:
- 0002-9939
- 1088-6826
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A note on micro-instability for Hamiltonian systems close to integrable
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2015'
...