## The singularity of symbolic matrices

Avi Wigderson

Herbert H. Maass Professor, School of Mathematics

February 16, 2016

While this lecture is a continuation of the lecture from last Tuesday, I will make it self contained. The main object of study of this talk are matrices whose entries are linear forms in a set of formal variables (over some field). The main problem is determining if a given such matrix is invertible or singular (over the appropriate field of rational functions). As it happens, this problem has a dual life; when the underlying variables commute, and when they do not.