Diophantine Approximation, Fractal Geometry and Related topics / Approximation diophantienne, géométrie fractale et sujets connexes

3 juin 2024, 08:50 → 7 juin 2024, 17:30 Europe/Paris

Auditorium (Marne)

Antoine Marnat (UPEC), Faustin Adiceam (UPEC), Richard Aoun (Université Gustave Eiffel)

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This conference aims to bring together specialists working in fields at the interface of Diophantine approximation, harmonic analysis and fractal geometry.

The scheduled is preliminary, and may change.

Wednesday afternoon will be free for participants to explore Paris, and a conference dinner will be held on Tuesday evening.

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Cette conférence vise à réunir des spécialistes travaillant dans les domaines à l’interface de l’approximation diophantienne, de l’analyse harmonique et de la géométrie fractale.

L'emploi du temps est provisoire et susceptible de changer.

Le mercredi après-midi sera laissé libre pour permettre aux participants d’explorer Paris et un dîner de conférence aura lieu mardi soir.

lundi 3 juin

08:50 → 09:20 Registration

09:20 → 09:30 Mot de bienvenue / Welcoming

09:30 → 10:30 Victor Beresnevich

TBA

10:30 → 11:00 Pause Café / Coffee Break

11:00 → 11:30 Sam Chow

Multiplicative approximation on hypersurfaces

11:30 → 11:40 Pause / Break

11:40 → 12:10 Simon Kristensen

14:10 → 15:10 Nikolay Moshchevitin

Geometry of the Best Approximations

15:10 → 15:20 Pause / Break

15:20 → 15:50 Reynold Fregoli

15:50 → 16:20 Pause Café / Coffee Break

16:20 → 16:50 Steven Robertson

16:50 → 17:00 Pause / Break

17:00 → 17:30 Niclas Technau

Rational Points Near Manifolds

I will report on recent results regarding the distribution of rational points near manifolds.

mardi 4 juin

09:30 → 10:30 Barak Weiss

Pushforwards of fractal measures and Diophantine approximation
on self-similar sets

Let \nu be a Bernoulli measure on a fractal in R^d generated by a finite collection of contracting similarities with no rotations and with rational coefficients; for instance, the usual coin tossing measure on Cantor's middle thirds set. Let a_t = diag (e^t ,..., e^t, e^-dt ), let U be its expanding horospherical group, which we identify with R^d , and let \bar \nu be the pushforward of \nu onto the space of lattices SL_d+1 (R)/SL_d+1 (Z), via the orbit map of the identity coset under U. In joint work in progress with Khalil and Luethi, we show that the pushforward of \bar \nu under a_t equidistributes as t tends to infinity, as do the pushforwards under more general one parameter subgroups. This generalizes a previous result of Khalil and Luethi. I will discuss some Diophantine applications and some probabilistic ideas used in the proof.

10:30 → 11:00 Pause Café / Coffee Break

11:00 → 11:30 Yitwah Cheung

11:30 → 11:40 Pause / Break

11:40 → 12:10 Erez Nesharim

The shifts of the Thue-Morse sequence have partial escape of mass

14:10 → 15:10 Damien Roy

Approximation rationnelle simultanée d'un nombre, de son carré et de son cube.

15:10 → 15:20 Pause / Break

15:20 → 15:50 Stéphane Fischler

15:50 → 16:20 Pause Café / Coffee Break

16:20 → 16:50 Taehyeong Kim

16:50 → 17:00 Pause / Break

17:00 → 17:30 Agamemnon Zafeiropoulos

A two-dimensional variant of Kaufman's measures in Diophantine Approximation

19:00 → 21:00 Diner de conférence / Conference diner

Les Noces de Jeannette
14, rue Favart - 75002 Paris

mercredi 5 juin

09:30 → 10:30 Dmitry Kleinbock

10:30 → 11:00 Pause Café / Coffee Break

11:00 → 11:30 Evgeniy Zorin

11:30 → 11:40 Pause / Break

11:40 → 12:10 René Pfitscher

Counting rational approximations in flag varieties

In the divergence case of Khintchine's theorem, Schmidt obtained an asymptotic formula for the number of rational approximations of bounded height to almost every real number. Using exponential mixing in the space of lattices, we prove versions of this theorem for intrinsic diophantine approximation on quadrics, grassmannians, and other examples of flag varieties.

jeudi 6 juin

09:30 → 10:30 Yann Bugeaud

10:30 → 11:00 Pause Café / Coffee Break

11:00 → 11:30 Stéphane Seuret

11:30 → 11:40 Pause / Break

11:40 → 12:10 Dorsa Vakilzadeh Hatefi

14:10 → 15:10 Cagri Sert

15:10 → 15:20 Pause / Break

15:20 → 15:50 Gaurav Aggarwal

15:50 → 16:20 Pause Café / Coffee Break

16:20 → 16:50 Shreyasi Datta

The set of badly approximable vectors in Diophantine approximation plays a significant role. In a recent work with Victor Beresnevich, Anish Ghosh, and Ben Ward, we developed a general framework to show that the set of badly approximable points has measure zero in a metric space equipped with certain natural measures. I will explain a few applications of our method in various number theoretic questions.

16:50 → 17:00 Pause / Break

17:00 → 17:30 Jiyoung Han

Quantitative Khintchine--Groshev theorem on S-arithmetic numbers

In this talk, I would like to introduce two analogs of S-arithmetic generalization of Diophantine approximation problems. One way to obtain quantitative results for Diophantine approximation over the real field is by utilizing Schmidt's counting theorem on the family of expanding Borel sets. We will explore how this approach can be extended to S-arithmetic Diophantine approximation, taking into consideration certain limitations.

vendredi 7 juin

09:30 → 10:30 Anish Ghosh

10:30 → 11:00 Pause Café / Coffee Break

11:00 → 11:30 Catalin Badea

Invariant Measures and Diophantine Approximation

11:30 → 11:40 Pause / Break

11:40 → 12:10 Prasuna Bandi

14:10 → 15:10 Stéphane Jaffard

15:10 → 15:20 Pause / Break

15:20 → 15:50 Arnaud Durand

Capacities and (large) intersections for random sets in metric spaces, with applications in dynamical Diophantine approximation

15:50 → 16:20 Pause Café / Coffee Break

16:20 → 16:50 Edouard Daviaud

Diophantine approximation on fractals

16:50 → 17:00 Pause / Break

17:00 → 17:30 Ioannis Tsokanos