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Fall 2014/ Spring 2015## Algebra / Logic Seminar

On Friday, February 13, at 4:00 p.m. in SE 215,

Antonio Lerario

(Univ. Claude Bernard Lyon 1)

will speak about

Complexity of Intersections of Real Quadrics and Discriminant Varieties

Abstract:In this talk I will focus on the problem of understanding the topology of an intersection X of real quadrics. I will introduce a new notion of algebro-geometric complexity (inspired by fewnomials and related considerations), using the discriminant in the space of quadratic forms. This leads to a "duality" between X and the set of singular quadrics in the linear system defining it. This approach is reminiscent of stratified Morse theory - topology and singularities interact in a controlled way, and in the case of intersections of three quadrics, we will see that the dual problem entails the first part of Hilbert's Sixteenth Problem.

All are welcome!

Last modified:by Robert Lubarsky