Video Lectures

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...

Galaxy clusters and cosmic filaments are the largest structures in the Universe. During mergers between clusters shocks and turbulence are driven in the intra-cluster-medium (ICM) and dissipate a fraction of their energy into particle acceleration...

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...

We review some recent progress towards  understanding   holographic duality for quantum gravity in asymptotically flat four-dimensional spacetimes. 

 We review some recent progress towards  understanding   holographic duality for quantum gravity in asymptotically flat four-dimensional spacetimes. 

An extension of Gromov compactness theorem ensures that any family of manifolds with convex boundaries, uniform bound on the dimension and uniform lower bound on the Ricci curvature is precompact in the Gromov-Hausdorff topology. In this talk, we...

In a joint work with Tianyi Zheng we show that the growth function of the first Grigorchuk group satisfies

lnlnvn/lnvn=a,

where a=log2/logx, x being a positive root of the polynomial x3−x2−2x−4. This is done by constructing measures with...

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...

Matthew Shipp is one of the most thoughtful, introspective and probing pianists working in the post-avantgarde-jazz world today. Known as a virtuosic improviser, Shipp's music moves subtly between musical material that he has previously composed and...

(work in progress with R. Rouquier) I will present a computational (yet conjectural) method to determine some decomposition matrices for finite groups of Lie type. These matrices encode how ordinary representations decompose when they are reduced to...