**Department of Mathematics**

TOPOLOGY SEMINAR

Carlsson's conjecture and variety of square-zero upper-triangular matrices

Abstract: Let k be an algebraically closed field of characteristic 2, A be a polynomial ring in m variables with coefficients in k, and (M,d) be a free, finitely generated DG-A-module. Carlsson conjectured that if the homology of M is nontrivial and finite dimensional, then the dimension of M is greater than or equal to 2^m.

` In this talk, we will state a new conjecture which implies Carlsson's conjecture and we wil provide some evidence for this conjecture. Then considering the fact that the differential d can be represented by a strictly upper triangular, square zero matrix, we will also discuss Borel orbits which contain such matrices and state a conjecture for the case in`

`two variables.`

**Date: ****Monday, November 28, 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.**