For decades, it was an open problem to show that every pair of almost commuting Hermitian matrices is close to commuting matrices, in a uniform way, independent of dimension, if we measure the size of matrices in the spectral norm.  Huaxin Lin's original proof that solved this problem was a tour-de-force of techniques in operator algebras.  A second proof was found by Friis and Rørdam that was used more basic tools from operator theory.  I will discuss that proof, as well has how that proof adapts to variations such as only looking at real symmetric matrices. 

This wll be in room 352.  If you cannot attend, a zoom link:  https://unm.zoom.us/j/94012736467  (UNM and FAMU domains only).