** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2015.05.12, 15:00--17:00

**Location:** Seminarraum 8, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "On the Birkhoff - von
Neumann theorem in type \(\mathrm{II}_1\) setting."

**Speaker:** Liviu Paunescu (IMAR, Bucharest)

**Abstract:**
The classic Birkhoff-von Neumann theorem states that the
set of doubly stochastic matrices is the convex hull of the
permutation matrices. In this presentation we study a possible
generalisation on this theorem in the type \(\mathrm{II}_1\) setting. Namely, we
replace a doubly stochastic matrix with a collection of measure
preserving partial isomorphisms, of the unit interval, with similar
properties.