Speaker: Pro. Mark Rudelson, University of Michigan

Time: 16:00-17:00 p.m., December 26, 2023, GMT+8

Venue: Room 77201, Jingchunyuan 78, BICMR

Abstract: 

The existence and the number of solutions of a system of polynomial equations in n variables over an algebraically closed field is a classical topic in algebraic geometry. Much less is known about the existence of solutions of a system of polynomial equations over reals. Any such problem can be reduced to a system of quadratic equations by introducing auxiliary variables. Due to the generality of the problem, a computationally efficient algorithm for determining whether a real solution of a system of quadratic equations exists is believed to be impossible. We will discuss a simple and efficient sufficient condition for the existence of a solution. While the problem and the condition are of algebraic nature, the approach lies entirely within the analysis/probability realm and relies on tools from Fourier analysis and concentration of measure. Joint work with Alexander Barvinok.

Source: Beijing International Center for Mathematical Reseach, PKU