## The singularity of symbolic matrices

Avi Wigderson

Herbert H. Maass Professor, School of Mathematics

February 9, 2016

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.