Geometry MMA Seminar: On Positivity for the Peterson Variety

Speaker: Rebecca Goldin, George Mason University

Title:   On Positivity for the Peterson Variety

Abstract:  “Positivity” is a phenomenon involving the intersection of subvarieties in the presence of enough structure to ensure that intersection points are positively oriented, among other generalizations. Such phenomena occur with frequency in the context of complex homogenous spaces such as flag varieties. In this talk, I will introduce and define positivity in a limited context, including some generalizations to the (torus) equivariant cohomology ring* of G/B, where G is a complex reductive group and B is a Borel subgroup. I will conclude with some recent results joint with L. Mihalcea and R. Singh, and separately with Brent Gorbutt, in which we show that Peterson varieties exhibit positivity phenomena. Time permitting, I will share some open questions about Hessenberg varieties, a large class of subvarieties of the flag manifold that include Peterson varieties.

* (Almost) everything you need to know about equivariant cohomology will be presented during the talk. 

Time: Monday, September 12, 2022 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208