Speaker: Raz Slutsky (Oxford)
Title: Random sparsification, torsion in homology, and fixed price
Abstract: Given a complicated geometric object, we often want to simplify it without losing information about the structure we are interested in. In this talk, I will describe a method for doing this by combining a random sparse set with a deterministic one, gaining some of the advantages of both. We will then see how this idea can be used to show that torsion in the first homology of higher-rank lattices grows subexponentially, answering a question of Abért, Gelander, and Nikolov and confirming the degree-one case of several conjectures. We will also use the same principle to give a new general criterion for a dynamical property known as fixed price one, which applies to a broad class of groups.