Name: Diophantine Approximation, Fractal Geometry and Related topics / Approximation diophantienne, géométrie fractale et sujets connexes
Start: 2024-06-03T08:50:00+02:00
End: 2024-06-07T17:30:00+02:00
Location: Marne

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

de lundi 3 juin 2024 (08:50) à vendredi 7 juin 2024 (17:30)

lundi 3 juin 2024

08:50 Registration
Registration
08:50 - 09:20
Room: Auditorium

09:20 Mot de bienvenue / Welcoming
Mot de bienvenue / Welcoming
09:20 - 09:30
Room: Auditorium

09:30 Victor Beresnevich
Victor Beresnevich
09:30 - 10:30
Room: Auditorium TBA

10:30 Pause Café / Coffee Break
Pause Café / Coffee Break
10:30 - 11:00
Room: 0B120

11:00 Sam Chow
Sam Chow
11:00 - 11:30
Room: Auditorium Multiplicative approximation on hypersurfaces

11:30 Pause / Break
Pause / Break
11:30 - 11:40
Room: 0B120

11:40 Simon Kristensen
Simon Kristensen
11:40 - 12:10
Room: Auditorium

14:10 Nikolay Moshchevitin
Nikolay Moshchevitin
14:10 - 15:10
Room: Auditorium Geometry of the Best Approximations

15:10 Pause / Break
Pause / Break
15:10 - 15:20
Room: 0B120

15:20 Reynold Fregoli
Reynold Fregoli
15:20 - 15:50
Room: Auditorium

15:50 Pause Café / Coffee Break
Pause Café / Coffee Break
15:50 - 16:20
Room: 0B120

16:20 Steven Robertson
Steven Robertson
16:20 - 16:50
Room: Auditorium

16:50 Pause / Break
Pause / Break
16:50 - 17:00
Room: 0B120

17:00 Niclas Technau
Niclas Technau
17:00 - 17:30
Room: Auditorium Rational Points Near Manifolds I will report on recent results regarding the distribution of rational points near manifolds.
mardi 4 juin 2024

09:30 Barak Weiss
Barak Weiss
09:30 - 10:30
Room: Auditorium 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 Pause Café / Coffee Break
Pause Café / Coffee Break
10:30 - 11:00
Room: 0B120

11:00 Yitwah Cheung
Yitwah Cheung
11:00 - 11:30
Room: Auditorium

11:30 Pause / Break
Pause / Break
11:30 - 11:40
Room: 0B120

11:40 Erez Nesharim
Erez Nesharim
11:40 - 12:10
Room: Auditorium The shifts of the Thue-Morse sequence have partial escape of mass

14:10 Damien Roy
Damien Roy
14:10 - 15:10
Room: Auditorium Approximation rationnelle simultanée d'un nombre, de son carré et de son cube.

15:10 Pause / Break
Pause / Break
15:10 - 15:20
Room: 0B120

15:20 Stéphane Fischler
Stéphane Fischler
15:20 - 15:50
Room: Auditorium

15:50 Pause Café / Coffee Break
Pause Café / Coffee Break
15:50 - 16:20
Room: 0B120

16:20 Taehyeong Kim
Taehyeong Kim
16:20 - 16:50
Room: Auditorium

16:50 Pause / Break
Pause / Break
16:50 - 17:00
Room: 0B120

17:00 Agamemnon Zafeiropoulos
Agamemnon Zafeiropoulos
17:00 - 17:30
Room: Auditorium A two-dimensional variant of Kaufman's measures in Diophantine Approximation

19:00 Diner de conférence / Conference diner
Diner de conférence / Conference diner
19:00 - 21:00
mercredi 5 juin 2024

09:30 Dmitry Kleinbock
Dmitry Kleinbock
09:30 - 10:30
Room: Auditorium

10:30 Pause Café / Coffee Break
Pause Café / Coffee Break
10:30 - 11:00
Room: 0B120

11:00 Evgeniy Zorin
Evgeniy Zorin
11:00 - 11:30
Room: Auditorium

11:30 Pause / Break
Pause / Break
11:30 - 11:40
Room: 0B120

11:40 René Pfitscher
René Pfitscher
11:40 - 12:10
Room: Auditorium 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 2024

09:30 Yann Bugeaud
Yann Bugeaud
09:30 - 10:30
Room: Auditorium

10:30 Pause Café / Coffee Break
Pause Café / Coffee Break
10:30 - 11:00
Room: 0B120

11:00 Stéphane Seuret
Stéphane Seuret
11:00 - 11:30
Room: Auditorium

11:30 Pause / Break
Pause / Break
11:30 - 11:40
Room: 0B120

11:40 Dorsa Vakilzadeh Hatefi
Dorsa Vakilzadeh Hatefi
11:40 - 12:10
Room: Auditorium

14:10 Cagri Sert
Cagri Sert
14:10 - 15:10
Room: Auditorium

15:10 Pause / Break
Pause / Break
15:10 - 15:20
Room: 0B120

15:20 Gaurav Aggarwal
Gaurav Aggarwal
15:20 - 15:50
Room: Auditorium

15:50 Pause Café / Coffee Break
Pause Café / Coffee Break
15:50 - 16:20
Room: 0B120

16:20 Shreyasi Datta
Shreyasi Datta
16:20 - 16:50
Room: Auditorium 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 Pause / Break
Pause / Break
16:50 - 17:00
Room: 0B120

17:00 Jiyoung Han
Jiyoung Han
17:00 - 17:30
Room: Auditorium 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 2024

09:30 Anish Ghosh
Anish Ghosh
09:30 - 10:30
Room: Auditorium

10:30 Pause Café / Coffee Break
Pause Café / Coffee Break
10:30 - 11:00
Room: 0B120

11:00 Catalin Badea
Catalin Badea
11:00 - 11:30
Room: Auditorium Invariant Measures and Diophantine Approximation

11:30 Pause / Break
Pause / Break
11:30 - 11:40
Room: 0B120

11:40 Prasuna Bandi
Prasuna Bandi
11:40 - 12:10
Room: Auditorium

14:10 Stéphane Jaffard
Stéphane Jaffard
14:10 - 15:10
Room: Auditorium

15:10 Pause / Break
Pause / Break
15:10 - 15:20
Room: 0B120

15:20 Arnaud Durand
Arnaud Durand
15:20 - 15:50
Room: Auditorium Capacities and (large) intersections for random sets in metric spaces, with applications in dynamical Diophantine approximation

15:50 Pause Café / Coffee Break
Pause Café / Coffee Break
15:50 - 16:20
Room: 0B120

16:20 Edouard Daviaud
Edouard Daviaud
16:20 - 16:50
Room: Auditorium Diophantine approximation on fractals

16:50 Pause / Break
Pause / Break
16:50 - 17:00
Room: 0B120

17:00 Ioannis Tsokanos
Ioannis Tsokanos
17:00 - 17:30
Room: Auditorium