Harry Pratt Judson Distinguished Service Professor
I am mostly interested in the Geometric Langlands program, which is a part of geometric representation theory. Below you can find Victor Ginzburg's description of the subject of geometric representation theory and the literature that he recommends.
Jointly with Mitya Boyarchenko (a student of mine) I am trying to develop the theory of character sheaves for unipotent groups. A unipotent group is a subgroup of the group of strictly triangular matrices defined by algebraic equations. Let \(G\) be a unipotent group over a finite field \(k\). For each positive integer n the points of \(G\) in the degree \(n\) extension of \(k\) form a finite group. Let \(X(n)\) be the set of its irreducible characters. Our goal is to understand \(X(n)\) for all \(n\) simultaneously in terms of certain perverse sheaves on \(G\), which are called character sheaves. Such a theory was developed by Lusztig for reductive groups \(G\). Inspired by a remarkable and short e-print by Lusztig, Mitya and I are trying to do this in the quite opposite case of unipotent groups.