## Geometry Seminar

**Date:** March 5, 2018

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Frank Sottile, Texas A&M University

**Title:** *Intersection Theory in Numerical Algebraic Geometry*

**Abstract:** I will describe how some ideas from intersection theory are useful in numerical algebraic geometry. The fundamental data structure in numerical algebraic geometry is that of a witness set, which is considered to be an instantiation of Weilâ€™s notion of a generic point. Reinterpreting a witness set in terms of duality of the intersection pairing in intersection theory leads to a generalization of the notion that makes sense on many spaces and leads to a general notion of a witness set. I will also describe how rational equivalence is linked to homotopy methods.

These notions are most productive for homogenous spaces, such as projective spaces, Grassmannians, and their products. After explaining the general theory, I will sketch what this means for the Grassmannian. This is joint work with Bates, Hauenstein, and Leykin.