Zeros of random polynomials

August 12 to August 16, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Norman Levenberg, Doron Lubinsky, Igor Pritsker, and Maxim Yattselev

Original Announcement

This workshop will be devoted to the zero distribution of random polynomials spanned by various deterministic bases. The prototypical classical example is the Kac polynomials, where the coefficients are i.i.d. real (or complex) Gaussian random variables, and the basis is given by standard monomials. Recent trends include studies of more general ensembles of random polynomials with non-Gaussian coefficients that are spanned by various polynomial bases, e.g., trigonometric and orthogonal polynomials.

The main topics for the workshop are

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos

Papers arising from the workshop:

Universality of the minimum modulus for random trigonometric polynomials
by  Nicholas A. Cook, Hoi H. Nguyen
Variance of real zeros of random orthogonal polynomials
by  Igor Pritsker, Doron Lubinsky
An asymptotic expansion for the expected number of real zeros of Kac-Geronimus polynomials
by  Hanan Aljubran, Maxim L. Yattselev
Exponential concentration for the number of roots of random trigonometric polynomials
by  Hoi H. Nguyen, Ofer Zeitouni
The minimum modulus of Gaussian trigonometric polynomials
by  Oren Yakir, Ofer Zeitouni