2020-21 Seminars

The aim of this talk is to show that C*-algebras are useful for studying stability of groups. In particular we will discuss some obstructions for Hilbert-Schmidt stability of groups, obtain a complete characterization of Hilbert-Schmidt stability...

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 “Garland’s method”, had several applications as a tool for proving...

Expander graphs in general, and Ramanujan graphs in particular, have played an important role in computer science and pure mathematics in the last four decades. In recent years the area of high dimensional expanders (i.e. simplical complexes with...

A recent line of work has focused on the following question: Can one prove strong unconditional lower bounds on the number of samples needed for learning under memory constraints? We study an extractor-based approach to proving such bounds for a...

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups $Sym(n)$ (in the sofic case) or the finite dimensional unitary...

I will discuss techniques, structural results, and open problems from two of my recent papers, in the context of a broader area of work on the motivating question: "how do we get the most from our data?"

In the first part of the talk, I will...

What combinatorial properties are likely to be satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball of fixed radius? What about any combinatorial rectangle of fixed side...

Let C be a class of groups. (For example, C is a class of all finite groups, or C is a class of all finite symmetric groups.) I give a definition of approximations of a group G by groups from C. For example, the groups approximable by symmetric...

Let X and Y be normed spaces. In functional analysis, a ``theorem on factorization through L2'' refers to the following type of statement: 

Every bounded linear operator A mapping X to Y (i.e. sup_x ||A(x)||_Y/||x||_X infinity), can be written as...

What can we say on a convex body from seeing its projections? In the 80s, Lutwak introduced a collection of measurements that capture this question. He called them the affine quermassintegrals. They are affine invariant analogues of the classical...