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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...

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...

In a joint work with Tianyi Zheng we show that the growth function of the first Grigorchuk group satisfies \[ \ln \ln v_n/\ln v_n = a, \] where $a = \log 2/\log x$, $x$ being a positive root of the polynomial $x^3-x^2-2x-4$. This is done by...

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...

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

Such factorization...

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

Such factorization...

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...