**Department of Mathematics**

TOPOLOGY SEMINAR

Variety of square-zero upper-triangular matrices-II

Abstract: Let k be an algebraically closed field of characteristic 2, A be the polynomial algebra in r variables with coefficients in k, and (M,d) be a finitely generated DG-A-module. Carlsson conjectured that if the homology of M is nontrivial and finite dimensional as a k-vector space then the dimension of M as a free A-module is greater than or equal to 2^r. In the second talk, we will continue to discuss the combinatorial method developed by Rothbach to stratify irreducible components of the variety of square-zero upper-triangular matrices. We will also discuss the subvarieties of matrices of submaximal rank in these irreducible components which were investigated by Karagueuzian, Oliver, and Ventura.

**Date: ****Monday, November 14, 2016**

**Time: ****13.40-14.30**

**Place: ****Mathematics Seminar Room,
SA-141**

**All are most cordially invited.
Tea and cookies will be served after the talk.**