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

**Time:** 2018.05.08, 15:15–17:00

**Location:** Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Almost commuting matrices
with respect to the rank metric."

**Speaker:** Łukasz
Grabowski (Lancaster University)

**Abstract:**
I will present my recent result with Gabor Elek, which deals
with the variant of the "Halmos problem" for the rank metric. A
particular case is as follows: if \(A\) and \(B\) are either unitary or
self-adjoint matrices that almost commute with respect to the rank
metric, then one can find commuting matrices \(C\) and \(D\) which are close
in the rank metric to the matrices \(A\) and \(B\) respectively.