---
_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
arxiv: 1
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. <i>Proceedings of the American Mathematical
    Society</i>. 2023;151(8):3401-3414. doi:<a href="https://doi.org/10.1090/proc/14361">10.1090/proc/14361</a>
  apa: Hua, B., Keller, M., Schwarz, M., &#38; Wirth, M. (2023). Sobolev-type inequalities
    and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/14361">https://doi.org/10.1090/proc/14361</a>
  chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type
    Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings
    of the American Mathematical Society</i>. American Mathematical Society, 2023.
    <a href="https://doi.org/10.1090/proc/14361">https://doi.org/10.1090/proc/14361</a>.
  ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and
    eigenvalue growth on graphs with finite measure,” <i>Proceedings of the American
    Mathematical Society</i>, 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.” <i>Proceedings of the American Mathematical Society</i>,
    vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:<a href="https://doi.org/10.1090/proc/14361">10.1090/proc/14361</a>.
  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: '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. <i>Proceedings of the American Mathematical
    Society</i>. 2023;151(3):907-914. doi:<a href="https://doi.org/10.1090/proc/15239">10.1090/proc/15239</a>
  apa: Balestrieri, F. (2023). Some remarks on strong approximation and applications
    to homogeneous spaces of linear algebraic groups. <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/15239">https://doi.org/10.1090/proc/15239</a>
  chicago: Balestrieri, Francesca. “Some Remarks on Strong Approximation and Applications
    to Homogeneous Spaces of Linear Algebraic Groups.” <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society, 2023. <a href="https://doi.org/10.1090/proc/15239">https://doi.org/10.1090/proc/15239</a>.
  ieee: F. Balestrieri, “Some remarks on strong approximation and applications to
    homogeneous spaces of linear algebraic groups,” <i>Proceedings of the American
    Mathematical Society</i>, 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.” <i>Proceedings of the American
    Mathematical Society</i>, vol. 151, no. 3, American Mathematical Society, 2023,
    pp. 907–14, doi:<a href="https://doi.org/10.1090/proc/15239">10.1090/proc/15239</a>.
  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: '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
arxiv: 1
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. <i>Proceedings
    of the American Mathematical Society</i>. 2021;149(1):37-52. doi:<a href="https://doi.org/10.1090/proc/15205">10.1090/proc/15205</a>
  apa: Brown, A., &#38; Romanov, A. (2021). Contravariant forms on Whittaker modules.
    <i>Proceedings of the American Mathematical Society</i>. American Mathematical
    Society. <a href="https://doi.org/10.1090/proc/15205">https://doi.org/10.1090/proc/15205</a>
  chicago: Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.”
    <i>Proceedings of the American Mathematical Society</i>. American Mathematical
    Society, 2021. <a href="https://doi.org/10.1090/proc/15205">https://doi.org/10.1090/proc/15205</a>.
  ieee: A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” <i>Proceedings
    of the American Mathematical Society</i>, 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.”
    <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1, American
    Mathematical Society, 2021, pp. 37–52, doi:<a href="https://doi.org/10.1090/proc/15205">10.1090/proc/15205</a>.
  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
arxiv: 1
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. <i>Proceedings of the American
    Mathematical Society</i>. 2019;147(11):4597-4604. doi:<a href="https://doi.org/10.1090/proc/14586">10.1090/proc/14586</a>
  apa: Li, P. (2019). A colimit of traces of reflection groups. <i>Proceedings of
    the American Mathematical Society</i>. AMS. <a href="https://doi.org/10.1090/proc/14586">https://doi.org/10.1090/proc/14586</a>
  chicago: Li, Penghui. “A Colimit of Traces of Reflection Groups.” <i>Proceedings
    of the American Mathematical Society</i>. AMS, 2019. <a href="https://doi.org/10.1090/proc/14586">https://doi.org/10.1090/proc/14586</a>.
  ieee: P. Li, “A colimit of traces of reflection groups,” <i>Proceedings of the American
    Mathematical Society</i>, 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.” <i>Proceedings of
    the American Mathematical Society</i>, vol. 147, no. 11, AMS, 2019, pp. 4597–604,
    doi:<a href="https://doi.org/10.1090/proc/14586">10.1090/proc/14586</a>.
  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. <i>Proceedings of the American Mathematical Society</i>.
    2015;144(4):1553-1560. doi:<a href="https://doi.org/10.1090/proc/12796">10.1090/proc/12796</a>
  apa: Bounemoura, A., &#38; Kaloshin, V. (2015). A note on micro-instability for
    Hamiltonian systems close to integrable. <i>Proceedings of the American Mathematical
    Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/12796">https://doi.org/10.1090/proc/12796</a>
  chicago: Bounemoura, Abed, and Vadim Kaloshin. “A Note on Micro-Instability for
    Hamiltonian Systems Close to Integrable.” <i>Proceedings of the American Mathematical
    Society</i>. American Mathematical Society, 2015. <a href="https://doi.org/10.1090/proc/12796">https://doi.org/10.1090/proc/12796</a>.
  ieee: A. Bounemoura and V. Kaloshin, “A note on micro-instability for Hamiltonian
    systems close to integrable,” <i>Proceedings of the American Mathematical Society</i>,
    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.” <i>Proceedings of the American Mathematical Society</i>,
    vol. 144, no. 4, American Mathematical Society, 2015, pp. 1553–60, doi:<a href="https://doi.org/10.1090/proc/12796">10.1090/proc/12796</a>.
  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'
...