Event № 699
ALL TALKS WILL BE HELD AT AMADO 232
Speakers and schedule :
09:30-10:00 Coffee and refreshments at the 8-th floor lounge
10:00-10:50 : Tali Pinsky (Technion Mathematics Department)
10:50-11:10 : Coffee break
11:10:-12:00 : Anish Ghosh (Tata Institute of Fundamental Research)
12:00-14:00 : Lunch
14:00-14:50 : Konstantin Golubev (Bar Ilan and Weizmann Institute)
14:50-15:10 : Coffee break
15:10-16:00 : Sanghoon Kwon (Korea Institute for Advanced Study)
TITLES AND ABSTRACTS
1) Tali Pinsky :
Title: An upper bound for volumes of geodesics
Abstract: Consider a closed geodesic gamma on a hyperbolic surface S, embedded in the unit tangent bundle of S. If gamma is filling its complement is a hyperbolic three manifold, and thus has a well defined volume. I will discuss how to use Ghys' template for the geodesic flow on the modular surface to obtain an upper bound for this volume in terms of the length of gamma. This is joint work with Maxime Bergeron and Lior Silberman.
2) Anish Ghosh :
Title: The metric theory of dense lattice orbits
Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study. In joint work with Alexander Gorodnik and Amos Nevo, we develop the first systematic metric theory for dense lattice orbits, including analogues of Khintchine's theorems.
3) Konstantin Golubev :
Title: Density theorems and almost diameter of quotient spaces
Abstract: We examine the typical distance between points in various quotient spaces. This question has an interesting approach inspired by the work of Lubetzky and Peres. They showed that the random walk on a graph expresses under the assumption of the graph being Ramanujan. We show that this condition can be relaxed to some density condition on the eigenvalues, and apply it to various settings. Joint work with Amitay Kamber.
4) Sanghoon Kwon :
Title: A combinatorial approach to the Littlewood conjecture in positive characteristic
Abstract: The Littlewood conjecture is an open problem in simultaneous Diophantine approximation of two real numbers. Similar problem in a field K of formal series over finite fields is also still open. This positive characteristic version of problem is equivalent to whether there is a certain bounded orbit of diagonal semigroup action on Bruhat-Tits building of PGL(3,K). We describe geometric properties of buildings associated to PGL(3,K), explore the combinatorics of the diagonal action on it and discuss how it helps to investigate the conjecture.