Évènement

Turgay Bayraktar
Sabanci University, Turquey
http://myweb.sabanciuniv.edu/tbayraktar/

Date(s) : 26/03/2018   iCal
10h00 - 11h00

Zero distribution of polynomials of high degree with random coefficients naturally appear, among others, in the context of quantum chaotic dynamics. A classical result asserts that if the coefficients are independent Gaussian random variables then zeros of random polynomials tend to accumulate near the unit circle on the complex plane. On the other hand, zeros of SU(2) polynomials are uniformly distributed on the Riemann sphere. While these results are consistent with Random Matrix Theory predictions they provide a new inside for the problem of quantum ergodicity. There are also higher dimensional generalizations of these results which form a relatively new field called Stochastic Kähler Geometry. In this talk, we will review some recent results on zero distribution of random polynomials and their generalization to compact Kähler manifolds. The main theme will be the universality of statistics of zeros of (generalized) random polynomials.

Catégories

• Séminaire