---
_id: '10765'
abstract:
- lang: eng
text: We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski
open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate
integral quadratic form in n>3 variables and m is a non-zero integer. This gives
asymptotic formulas for the density of integral points taking coprime polynomial
values, which is a quantitative version of the arithmetic purity of strong approximation
property off infinity for affine quadrics.
acknowledgement: "We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg
for their interest in our\r\nwork. We would like to address our gratitude to Ulrich
Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt
to Tim Browning for an enlightening discussion and to the anonymous referees for
critical comments, which lead to overall improvements of various preliminary versions
of this paper. Part of this work was carried out and reported during a visit to
the University of Science and Technology of China. We thank Yongqi Liang for offering
warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium.
The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft."
article_number: '108236'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yang
full_name: Cao, Yang
last_name: Cao
- first_name: Zhizhong
full_name: Huang, Zhizhong
id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51
last_name: Huang
citation:
ama: Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric
sieve for affine quadrics. Advances in Mathematics. 2022;398(3). doi:10.1016/j.aim.2022.108236
apa: Cao, Y., & Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood
property and geometric sieve for affine quadrics. Advances in Mathematics.
Elsevier. https://doi.org/10.1016/j.aim.2022.108236
chicago: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood
Property and Geometric Sieve for Affine Quadrics.” Advances in Mathematics.
Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108236.
ieee: Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and
geometric sieve for affine quadrics,” Advances in Mathematics, vol. 398,
no. 3. Elsevier, 2022.
ista: Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and
geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.
mla: Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property
and Geometric Sieve for Affine Quadrics.” Advances in Mathematics, vol.
398, no. 3, 108236, Elsevier, 2022, doi:10.1016/j.aim.2022.108236.
short: Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).
date_created: 2022-02-20T23:01:30Z
date_published: 2022-03-26T00:00:00Z
date_updated: 2023-08-02T14:24:18Z
day: '26'
department:
- _id: TiBr
doi: 10.1016/j.aim.2022.108236
external_id:
arxiv:
- '2003.07287'
isi:
- '000792517300014'
intvolume: ' 398'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2003.07287
month: '03'
oa: 1
oa_version: Preprint
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: Arithmetic purity of the Hardy-Littlewood property and geometric sieve for
affine quadrics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 398
year: '2022'
...
---
_id: '11717'
abstract:
- lang: eng
text: "We study rigidity of rational maps that come from Newton's root finding method
for polynomials of arbitrary degrees. We establish dynamical rigidity of these
maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit
can be distinguished in combinatorial terms from all other orbits), or the orbit
of this point eventually lands in the filled-in Julia set of a polynomial-like
restriction of the original map. As a corollary, we show that the Julia sets of
Newton maps in many non-trivial cases are locally connected; in particular, every
cubic Newton map without Siegel points has locally connected Julia set.\r\nIn
the parameter space of Newton maps of arbitrary degree we obtain the following
rigidity result: any two combinatorially equivalent Newton maps are quasiconformally
conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable,
or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized
renormalization concept called “complex box mappings” for which we extend a dynamical
rigidity result by Kozlovski and van Strien so as to include irrationally indifferent
and renormalizable situations."
acknowledgement: 'We are grateful to a number of colleagues for helpful and inspiring
discussions during the time when we worked on this project, in particular Dima Dudko,
Misha Hlushchanka, John Hubbard, Misha Lyubich, Oleg Kozlovski, and Sebastian van
Strien. Finally, we would like to thank our dynamics research group for numerous
helpful and enjoyable discussions: Konstantin Bogdanov, Roman Chernov, Russell Lodge,
Steffen Maaß, David Pfrang, Bernhard Reinke, Sergey Shemyakov, and Maik Sowinski.
We gratefully acknowledge support by the Advanced Grant “HOLOGRAM” (#695 621) of
the European Research Council (ERC), as well as hospitality of Cornell University
in the spring of 2018 while much of this work was prepared. The first-named author
also acknowledges the support of the ERC Advanced Grant “SPERIG” (#885 707).'
article_number: '108591'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Kostiantyn
full_name: Drach, Kostiantyn
id: fe8209e2-906f-11eb-847d-950f8fc09115
last_name: Drach
orcid: 0000-0002-9156-8616
- first_name: Dierk
full_name: Schleicher, Dierk
last_name: Schleicher
citation:
ama: Drach K, Schleicher D. Rigidity of Newton dynamics. Advances in Mathematics.
2022;408(Part A). doi:10.1016/j.aim.2022.108591
apa: Drach, K., & Schleicher, D. (2022). Rigidity of Newton dynamics. Advances
in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108591
chicago: Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.”
Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108591.
ieee: K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” Advances in
Mathematics, vol. 408, no. Part A. Elsevier, 2022.
ista: Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics.
408(Part A), 108591.
mla: Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances
in Mathematics, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:10.1016/j.aim.2022.108591.
short: K. Drach, D. Schleicher, Advances in Mathematics 408 (2022).
date_created: 2022-08-01T17:08:16Z
date_published: 2022-10-29T00:00:00Z
date_updated: 2023-08-03T12:36:07Z
day: '29'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1016/j.aim.2022.108591
ec_funded: 1
external_id:
isi:
- '000860924200005'
file:
- access_level: open_access
checksum: 2710e6f5820f8c20a676ddcbb30f0e8d
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T07:39:09Z
date_updated: 2023-02-02T07:39:09Z
file_id: '12474'
file_name: 2022_AdvancesMathematics_Drach.pdf
file_size: 2164036
relation: main_file
success: 1
file_date_updated: 2023-02-02T07:39:09Z
has_accepted_license: '1'
intvolume: ' 408'
isi: 1
issue: Part A
keyword:
- General Mathematics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rigidity of Newton dynamics
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: 408
year: '2022'
...
---
_id: '9036'
abstract:
- lang: eng
text: In this short note, we prove that the square root of the quantum Jensen-Shannon
divergence is a true metric on the cone of positive matrices, and hence in particular
on the quantum state space.
acknowledgement: D. Virosztek was supported by the European Union's Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294,
and partially supported by the Hungarian National Research, Development and Innovation
Office (NKFIH) via grants no. K124152, and no. KH129601.
article_number: '107595'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595
apa: Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595
chicago: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.
ieee: D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,”
Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.
ista: Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 380(3), 107595.
mla: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.
short: D. Virosztek, Advances in Mathematics 380 (2021).
date_created: 2021-01-22T17:55:17Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2023-08-07T13:34:48Z
day: '26'
department:
- _id: LaEr
doi: 10.1016/j.aim.2021.107595
ec_funded: 1
external_id:
arxiv:
- '1910.10447'
isi:
- '000619676100035'
intvolume: ' 380'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.10447
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: The metric property of the quantum Jensen-Shannon divergence
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 380
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: '9588'
abstract:
- lang: eng
text: 'Consider the sum X(ξ)=∑ni=1aiξi , where a=(ai)ni=1 is a sequence of non-zero
reals and ξ=(ξi)ni=1 is a sequence of i.i.d. Rademacher random variables (that
is, Pr[ξi=1]=Pr[ξi=−1]=1/2 ). The classical Littlewood-Offord problem asks for
the best possible upper bound on the concentration probabilities Pr[X=x] . In
this paper we study a resilience version of the Littlewood-Offord problem: how
many of the ξi is an adversary typically allowed to change without being able
to force concentration on a particular value? We solve this problem asymptotically,
and present a few interesting open problems.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Afonso S.
full_name: Bandeira, Afonso S.
last_name: Bandeira
- first_name: Asaf
full_name: Ferber, Asaf
last_name: Ferber
- 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: Bandeira AS, Ferber A, Kwan MA. Resilience for the Littlewood–Offord problem.
Advances in Mathematics. 2017;319:292-312. doi:10.1016/j.aim.2017.08.031
apa: Bandeira, A. S., Ferber, A., & Kwan, M. A. (2017). Resilience for the Littlewood–Offord
problem. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2017.08.031
chicago: Bandeira, Afonso S., Asaf Ferber, and Matthew Alan Kwan. “Resilience for
the Littlewood–Offord Problem.” Advances in Mathematics. Elsevier, 2017.
https://doi.org/10.1016/j.aim.2017.08.031.
ieee: A. S. Bandeira, A. Ferber, and M. A. Kwan, “Resilience for the Littlewood–Offord
problem,” Advances in Mathematics, vol. 319. Elsevier, pp. 292–312, 2017.
ista: Bandeira AS, Ferber A, Kwan MA. 2017. Resilience for the Littlewood–Offord
problem. Advances in Mathematics. 319, 292–312.
mla: Bandeira, Afonso S., et al. “Resilience for the Littlewood–Offord Problem.”
Advances in Mathematics, vol. 319, Elsevier, 2017, pp. 292–312, doi:10.1016/j.aim.2017.08.031.
short: A.S. Bandeira, A. Ferber, M.A. Kwan, Advances in Mathematics 319 (2017) 292–312.
date_created: 2021-06-22T11:51:27Z
date_published: 2017-10-15T00:00:00Z
date_updated: 2023-02-23T14:01:57Z
day: '15'
doi: 10.1016/j.aim.2017.08.031
extern: '1'
external_id:
arxiv:
- '1609.08136'
intvolume: ' 319'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1609.08136
month: '10'
oa: 1
oa_version: Preprint
page: 292-312
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Resilience for the Littlewood–Offord problem
type: journal_article
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 319
year: '2017'
...
---
_id: '8511'
abstract:
- lang: eng
text: "Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse,
Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer.
Math. Soc., 1970, pp. 191–202; S. Newhouse,\r\nDiffeomorphisms with infinitely
many sinks, Topology 13 (1974) 9–18; S. Newhouse, The abundance of\r\nwild hyperbolic
sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études
Sci.\r\n50 (1979) 101–151]. It turns out that in the space of Cr smooth diffeomorphisms
Diffr(M) of a compact\r\nsurface M there is an open set U such that a Baire generic
diffeomorphism f ∈ U has infinitely many coexisting sinks. In this paper we make
a step towards understanding “how often does a surface diffeomorphism\r\nhave
infinitely many sinks.” Our main result roughly says that with probability one
for any positive D a\r\nsurface diffeomorphism has only finitely many localized
sinks either of cyclicity bounded by D or those\r\nwhose period is relatively
large compared to its cyclicity. It verifies a particular case of Palis’ Conjecture\r\nsaying
that even though diffeomorphisms with infinitely many coexisting sinks are Baire
generic, they have\r\nprobability zero.\r\nOne of the key points of the proof
is an application of Newton Interpolation Polynomials to study the dynamics initiated
in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth
of the number\r\nof periodic points for prevalent diffeomorphisms I, Ann. of Math.,
in press, 92 pp.; V. Kaloshin, A stretched\r\nexponential bound on the rate of
growth of the number of periodic points for prevalent diffeomorphisms II,\r\npreprint,
85 pp.]."
article_processing_charge: No
article_type: original
author:
- first_name: A.
full_name: Gorodetski, A.
last_name: Gorodetski
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Gorodetski A, Kaloshin V. How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances
in Mathematics. 2007;208(2):710-797. doi:10.1016/j.aim.2006.03.012
apa: Gorodetski, A., & Kaloshin, V. (2007). How often surface diffeomorphisms
have infinitely many sinks and hyperbolicity of periodic points near a homoclinic
tangency. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2006.03.012
chicago: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms
Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic
Tangency.” Advances in Mathematics. Elsevier, 2007. https://doi.org/10.1016/j.aim.2006.03.012.
ieee: A. Gorodetski and V. Kaloshin, “How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency,” Advances
in Mathematics, vol. 208, no. 2. Elsevier, pp. 710–797, 2007.
ista: Gorodetski A, Kaloshin V. 2007. How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances
in Mathematics. 208(2), 710–797.
mla: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have
Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.”
Advances in Mathematics, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:10.1016/j.aim.2006.03.012.
short: A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797.
date_created: 2020-09-18T10:48:27Z
date_published: 2007-01-30T00:00:00Z
date_updated: 2021-01-12T08:19:47Z
day: '30'
doi: 10.1016/j.aim.2006.03.012
extern: '1'
intvolume: ' 208'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '01'
oa_version: None
page: 710-797
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: How often surface diffeomorphisms have infinitely many sinks and hyperbolicity
of periodic points near a homoclinic tangency
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 208
year: '2007'
...