First meeting, Technion, 8.12.19, Amado building room 232
Random walks on tori and an application to normal numbers in self-similar sets.
We show that under certain conditions, random walks on a d-dim torus by affine expanding maps have a unique stationary measure. We then use this result to show that given an IFS of contracting similarity maps of the real line with a uniform contraction ratio 1/D, where D is some integer > 1, under some suitable condition, almost every point in the attractor of the given IFS (w.r.t. a natural measure) is normal to base D.
Joint work with Arijit Ganguly and Barak Weiss.
Vanishing of cohomology for groups acting on buildings
In his seminal paper from 1973, Garland introduced a machinery for proving vanishing of group cohomology for groups acting on Bruhat-Tits buildings. This machinery, known today as the Garland method, had several applications as a tool for proving rigidity results (e.g., proving Kazhdan property (T) or, more recently, group stability results). In my talk, I will discuss various generalizations of the Garland method. Namely, a sharp version of the Garland method for affine buildings and vanishing results with coefficients in Banach spaces. Time permitting, I will also discuss applications to group stability.
Parts of this talk are based on a joint works with Z. Grinbaum-Reizis and with A. Lubotzky.
Random walks on ultra discrete-limits
We present a link between ultra-discrete versions of partial differential equations and groups. The crucial point of this construction is the translation of the equations into the language of finite automata and the analysis of the random walk operator on the space of solutions.
Rigidity Phenomena In Non-Commutative Ergodic Theory
We study group actions from the point of view of their associated C* and von Neumann algebras. In particular, we are interested in rigidity phenomena of these algebras. We establish some framework in which such rigidity occur and draw conclusions about unitary representations and minimal amenability of certain von Neumann algebras.
Joint work with Mehrdad Kalantar.
You are cordially invited.
The support of BGU Center for advanced studies in mathematics is gratefully acknowledged.
