TOPOLOGY SEMINAR

**"****The Variety of Square
Zero Matrices****"**

By

**Abstract: **** ****In this talk, motivated by the algebraic version of
the Carlsson's conjecture which states if k is an
algebraic closure of F _{2}, R=k[x_{1},…,x_{r}] and (M, ∂)_{ }is a
free, finitely generated DG-R module and its homology is nonzero, finite
dimensional as a k-vector space, then the rank of M over
R is at least 2^{r}, we consider the variety of strictly upper
triangular square zero 2nx2n matrices. We will describe the irreducible
components of this variety and decompose into orbits of the Borel
group by using Rothbach's technique. Moreover, we fix
a particular irreducible component of this variety and study the structure of
the subvariety of matrices of rank n in this component
by using Karagueuzian, Oliver and Ventura's idea.**

**Date: ****Monday, December 21, 2015**

**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.**