Pure Math Department Colloquium
Jointly held with the Probability seminar series
Mark Rudelson
University of Michigan
Room: MC 5501
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 and efficient sufficient condition for the existence of a solution. While the problem and the condition are of algebraic nature, the proof relies on Fourier analysis and concentration of measure.
Joint work with Alexander Barvinok.
Location Information
200 University Avenue West
Waterloo, ON, CA N2L 3G1
