---
_id: '8682'
abstract:
- lang: eng
text: It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous
for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover,
for such varieties it follows from a general conjecture of Colliot-Thélène that
the Brauer--Manin obstruction to the Hasse principle should be the only one, so
that the Hasse principle is expected to hold. Working over the field of rational
numbers and ordering Fano hypersurfaces of fixed degree and dimension by height,
we prove that almost every such hypersurface satisfies the Hasse principle provided
that the dimension is at least 3. This proves a conjecture of Poonen and Voloch
in every case except for cubic surfaces.
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: Pierre Le
full_name: Boudec, Pierre Le
last_name: Boudec
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces.
Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3
apa: Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle
for random Fano hypersurfaces. Annals of Mathematics. Princeton University.
https://doi.org/10.4007/annals.2023.197.3.3
chicago: Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle
for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University,
2023. https://doi.org/10.4007/annals.2023.197.3.3.
ieee: T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random
Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton
University, pp. 1115–1203, 2023.
ista: Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano
hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.
mla: Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.”
Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp.
1115–203, doi:10.4007/annals.2023.197.3.3.
short: T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.
date_created: 2020-10-19T14:28:50Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-08-11T11:59:49Z
day: '01'
department:
- _id: TiBr
doi: 10.4007/annals.2023.197.3.3
external_id:
arxiv:
- '2006.02356'
isi:
- '000966611000003'
oaworkID:
- w3033938593
intvolume: ' 197'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.02356
month: '05'
oa: 1
oa_version: Preprint
oaworkID: 1
page: 1115-1203
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/when-is-necessary-sufficient/
status: public
title: The Hasse principle for random Fano hypersurfaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 197
year: '2023'
...
---
_id: '8421'
abstract:
- lang: eng
text: 'The classical Birkhoff conjecture claims that the boundary of a strictly
convex integrable billiard table is necessarily an ellipse (or a circle as a special
case). In this article we prove a complete local version of this conjecture: a
small integrable perturbation of an ellipse must be an ellipse. This extends and
completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains
were considered. One of the crucial ideas in the proof is to extend action-angle
coordinates for elliptic billiards into complex domains (with respect to the angle),
and to thoroughly analyze the nature of their complex singularities. As an application,
we are able to prove some spectral rigidity results for elliptic domains.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards.
Annals of Mathematics. 2018;188(1):315-380. doi:10.4007/annals.2018.188.1.6
apa: Kaloshin, V., & Sorrentino, A. (2018). On the local Birkhoff conjecture
for convex billiards. Annals of Mathematics. Annals of Mathematics, Princeton
U. https://doi.org/10.4007/annals.2018.188.1.6
chicago: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics. Annals of Mathematics, Princeton
U, 2018. https://doi.org/10.4007/annals.2018.188.1.6.
ieee: V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex
billiards,” Annals of Mathematics, vol. 188, no. 1. Annals of Mathematics,
Princeton U, pp. 315–380, 2018.
ista: Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex
billiards. Annals of Mathematics. 188(1), 315–380.
mla: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics, vol. 188, no. 1, Annals of
Mathematics, Princeton U, 2018, pp. 315–80, doi:10.4007/annals.2018.188.1.6.
short: V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.
date_created: 2020-09-17T10:42:22Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '01'
doi: 10.4007/annals.2018.188.1.6
extern: '1'
external_id:
arxiv:
- '1612.09194'
intvolume: ' 188'
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.09194
month: '07'
oa: 1
oa_version: Preprint
page: 315-380
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics, Princeton U
quality_controlled: '1'
status: public
title: On the local Birkhoff conjecture for convex billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 188
year: '2018'
...
---
_id: '8427'
abstract:
- lang: eng
text: We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex
domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all
deformations among domains in the same class that preserve the length of all periodic
orbits of the associated billiard flow must necessarily be isometric deformations.
This gives a partial answer to a question of P. Sarnak.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Qiaoling
full_name: Wei, Qiaoling
last_name: Wei
citation:
ama: De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle. Annals of Mathematics. 2017;186(1):277-314.
doi:10.4007/annals.2017.186.1.7
apa: De Simoi, J., Kaloshin, V., & Wei, Q. (2017). Dynamical spectral rigidity
among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics.
Annals of Mathematics. https://doi.org/10.4007/annals.2017.186.1.7
chicago: De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral
Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” Annals
of Mathematics. Annals of Mathematics, 2017. https://doi.org/10.4007/annals.2017.186.1.7.
ieee: J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle,” Annals of Mathematics, vol.
186, no. 1. Annals of Mathematics, pp. 277–314, 2017.
ista: De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.
mla: De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly
Convex Domains Close to a Circle.” Annals of Mathematics, vol. 186, no.
1, Annals of Mathematics, 2017, pp. 277–314, doi:10.4007/annals.2017.186.1.7.
short: J. De Simoi, V. Kaloshin, Q. Wei, Annals of Mathematics 186 (2017) 277–314.
date_created: 2020-09-17T10:46:42Z
date_published: 2017-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:12Z
day: '01'
doi: 10.4007/annals.2017.186.1.7
extern: '1'
external_id:
arxiv:
- '1606.00230'
intvolume: ' 186'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1606.00230
month: '07'
oa: 1
oa_version: Preprint
page: 277-314
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics
quality_controlled: '1'
status: public
title: Dynamical spectral rigidity among Z2-symmetric strictly convex domains close
to a circle
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 186
year: '2017'
...
---
_id: '8496'
article_processing_charge: No
article_type: original
author:
- first_name: Artur
full_name: Avila, Artur
last_name: Avila
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Avila A, De Simoi J, Kaloshin V. An integrable deformation of an ellipse of
small eccentricity is an ellipse. Annals of Mathematics. 2016;184(2):527-558.
doi:10.4007/annals.2016.184.2.5
apa: Avila, A., De Simoi, J., & Kaloshin, V. (2016). An integrable deformation
of an ellipse of small eccentricity is an ellipse. Annals of Mathematics.
Princeton University Press. https://doi.org/10.4007/annals.2016.184.2.5
chicago: Avila, Artur, Jacopo De Simoi, and Vadim Kaloshin. “An Integrable Deformation
of an Ellipse of Small Eccentricity Is an Ellipse.” Annals of Mathematics.
Princeton University Press, 2016. https://doi.org/10.4007/annals.2016.184.2.5.
ieee: A. Avila, J. De Simoi, and V. Kaloshin, “An integrable deformation of an ellipse
of small eccentricity is an ellipse,” Annals of Mathematics, vol. 184,
no. 2. Princeton University Press, pp. 527–558, 2016.
ista: Avila A, De Simoi J, Kaloshin V. 2016. An integrable deformation of an ellipse
of small eccentricity is an ellipse. Annals of Mathematics. 184(2), 527–558.
mla: Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity
Is an Ellipse.” Annals of Mathematics, vol. 184, no. 2, Princeton University
Press, 2016, pp. 527–58, doi:10.4007/annals.2016.184.2.5.
short: A. Avila, J. De Simoi, V. Kaloshin, Annals of Mathematics 184 (2016) 527–558.
date_created: 2020-09-18T10:46:22Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:40Z
day: '01'
doi: 10.4007/annals.2016.184.2.5
extern: '1'
intvolume: ' 184'
issue: '2'
language:
- iso: eng
month: '09'
oa_version: None
page: 527-558
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
status: public
title: An integrable deformation of an ellipse of small eccentricity is an ellipse
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 184
year: '2016'
...
---
_id: '8503'
abstract:
- lang: eng
text: We prove there are finitely many isometry classes of planar central configurations
(also called relative equilibria) in the Newtonian 5-body problem, except perhaps
if the 5-tuple of positive masses belongs to a given codimension 2 subvariety
of the mass space.
article_processing_charge: No
article_type: original
author:
- first_name: Alain
full_name: Albouy, Alain
last_name: Albouy
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Albouy A, Kaloshin V. Finiteness of central configurations of five bodies in
the plane. Annals of Mathematics. 2012;176(1):535-588. doi:10.4007/annals.2012.176.1.10
apa: Albouy, A., & Kaloshin, V. (2012). Finiteness of central configurations
of five bodies in the plane. Annals of Mathematics. Princeton University
Press. https://doi.org/10.4007/annals.2012.176.1.10
chicago: Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations
of Five Bodies in the Plane.” Annals of Mathematics. Princeton University
Press, 2012. https://doi.org/10.4007/annals.2012.176.1.10.
ieee: A. Albouy and V. Kaloshin, “Finiteness of central configurations of five bodies
in the plane,” Annals of Mathematics, vol. 176, no. 1. Princeton University
Press, pp. 535–588, 2012.
ista: Albouy A, Kaloshin V. 2012. Finiteness of central configurations of five bodies
in the plane. Annals of Mathematics. 176(1), 535–588.
mla: Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of
Five Bodies in the Plane.” Annals of Mathematics, vol. 176, no. 1, Princeton
University Press, 2012, pp. 535–88, doi:10.4007/annals.2012.176.1.10.
short: A. Albouy, V. Kaloshin, Annals of Mathematics 176 (2012) 535–588.
date_created: 2020-09-18T10:47:24Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.4007/annals.2012.176.1.10
extern: '1'
intvolume: ' 176'
issue: '1'
language:
- iso: eng
month: '07'
oa_version: None
page: 535-588
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
status: public
title: Finiteness of central configurations of five bodies in the plane
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 176
year: '2012'
...
---
_id: '8512'
abstract:
- lang: eng
text: "For diffeomorphisms of smooth compact finite-dimensional manifolds, we consider
the problem of how fast the number of periodic points with period n grows as a
function of n. In many familiar cases (e.g., Anosov systems) the growth is exponential,
but arbitrarily fast growth is possible; in fact, the first author has shown that
arbitrarily fast growth is topologically (Baire) generic for C2 or smoother diffeomorphisms.
In the present work we show that, by contrast, for a measure-theoretic notion
of genericity we call “prevalence”, the growth is not much faster than exponential.
Specifically, we show that for each ρ,δ>0, there is a prevalent set of C1+ρ (or
smoother) diffeomorphisms for which the number of periodic n points is bounded
above by exp(Cn1+δ) for some C independent of n. We also obtain a related bound
on the decay of hyperbolicity of the periodic points as a function of n, and obtain
the same results for 1-dimensional endomorphisms. The contrast between topologically
generic and measure-theoretically generic behavior for the growth of the number
of periodic points and the decay of their hyperbolicity show this to be a subtle
and complex phenomenon, reminiscent of KAM theory. Here in Part I we state our
results and describe the methods we use. We complete most of the proof in the
1-dimensional C2-smooth case and outline the remaining steps, deferred to Part
II, that are needed to establish the general case.\r\n\r\nThe novel feature of
the approach we develop in this paper is the introduction of Newton Interpolation
Polynomials as a tool for perturbing trajectories of iterated maps."
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Brian
full_name: Hunt, Brian
last_name: Hunt
citation:
ama: Kaloshin V, Hunt B. Stretched exponential estimates on growth of the number
of periodic points for prevalent diffeomorphisms I. Annals of Mathematics.
2007;165(1):89-170. doi:10.4007/annals.2007.165.89
apa: Kaloshin, V., & Hunt, B. (2007). Stretched exponential estimates on growth
of the number of periodic points for prevalent diffeomorphisms I. Annals of
Mathematics. Princeton University Press. https://doi.org/10.4007/annals.2007.165.89
chicago: Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth
of the Number of Periodic Points for Prevalent Diffeomorphisms I.” Annals of
Mathematics. Princeton University Press, 2007. https://doi.org/10.4007/annals.2007.165.89.
ieee: V. Kaloshin and B. Hunt, “Stretched exponential estimates on growth of the
number of periodic points for prevalent diffeomorphisms I,” Annals of Mathematics,
vol. 165, no. 1. Princeton University Press, pp. 89–170, 2007.
ista: Kaloshin V, Hunt B. 2007. Stretched exponential estimates on growth of the
number of periodic points for prevalent diffeomorphisms I. Annals of Mathematics.
165(1), 89–170.
mla: Kaloshin, Vadim, and Brian Hunt. “Stretched Exponential Estimates on Growth
of the Number of Periodic Points for Prevalent Diffeomorphisms I.” Annals of
Mathematics, vol. 165, no. 1, Princeton University Press, 2007, pp. 89–170,
doi:10.4007/annals.2007.165.89.
short: V. Kaloshin, B. Hunt, Annals of Mathematics 165 (2007) 89–170.
date_created: 2020-09-18T10:48:33Z
date_published: 2007-01-01T00:00:00Z
date_updated: 2021-01-12T08:19:48Z
day: '01'
doi: 10.4007/annals.2007.165.89
extern: '1'
intvolume: ' 165'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 89-170
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
status: public
title: Stretched exponential estimates on growth of the number of periodic points
for prevalent diffeomorphisms I
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 165
year: '2007'
...
---
_id: '8526'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Kaloshin V. An extension of the Artin-Mazur theorem. The Annals of Mathematics.
1999;150(2):729-741. doi:10.2307/121093
apa: Kaloshin, V. (1999). An extension of the Artin-Mazur theorem. The Annals
of Mathematics. JSTOR. https://doi.org/10.2307/121093
chicago: Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” The Annals
of Mathematics. JSTOR, 1999. https://doi.org/10.2307/121093.
ieee: V. Kaloshin, “An extension of the Artin-Mazur theorem,” The Annals of Mathematics,
vol. 150, no. 2. JSTOR, pp. 729–741, 1999.
ista: Kaloshin V. 1999. An extension of the Artin-Mazur theorem. The Annals of Mathematics.
150(2), 729–741.
mla: Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” The Annals of
Mathematics, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:10.2307/121093.
short: V. Kaloshin, The Annals of Mathematics 150 (1999) 729–741.
date_created: 2020-09-18T10:50:28Z
date_published: 1999-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '01'
doi: 10.2307/121093
extern: '1'
intvolume: ' 150'
issue: '2'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa_version: None
page: 729-741
publication: The Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: JSTOR
quality_controlled: '1'
status: public
title: An extension of the Artin-Mazur theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 150
year: '1999'
...