**SMS scnews item created by Stephan Tillmann at Tue 18 Aug 2015 1140**

Type: Seminar

Distribution: World

Expiry: 17 Nov 2015

**Calendar1: 19 Aug 2015 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry & Topology

# Recurrence, measure rigidity and characteristic polynomial patterns in difference sets of matrices

### Sasha Fish

Wednesday 19 August 2015 from 11:00–12:00 in Carslaw 535A

Please join us for lunch after the talk!

**Abstract:**
We present a new approach for establishing the recurrence of a
set, through measure rigidity of associated action. Recall, that a subset \(S\)
of integers (or of another amenable group \(G\)) is recurrent if for every set \(E\)
in integers (in \(G\)) of positive density the sets \(S\) and \(E-E\) intersect
non-trivially. By use of measure rigidity results of Benoist-Quint for
algebraic actions on homogeneous spaces and our method, we prove that for
every set \(E\) of positive density inside traceless square matrices with
integer values, there exists \(k\ge 1\) such that the set of characteristic
polynomials of matrices in \(E-E\) contains ALL characteristic polynomials of
traceless matrices divisible by \(k\). This talk is based on a joint work with
M. Bjorklund (Chalmers)