Your browser is unsupported

We recommend using the latest version of IE11, Edge, Chrome, Firefox or Safari.

Feb 16 2024

Departmental Colloquium: When a system of real quadratic equations has a solution, by Mark Rudelson

February 16, 2024

3:00 PM - 3:50 PM

Location

636 SEO

Address

Chicago, IL

Mark Rudelson (University of Michigan): When a system of real quadratic equations has a solution

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 sufficient condition for the existence of a solution which can be efficiently checked. 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.

Local host: Marcus Michelen

Please click here to make changes to, or delete, this seminar announcement.

Contact

Osama Khalil

Date posted

Mar 1, 2024

Date updated

Mar 1, 2024

Speakers