**Date & Time:** Monday, February 22, 2016, 11:30.

**Venue:** Ramanujan Hall

**Speaker:**Manjunath Krishnapur,

Indian Institute of Science, Bangalore

**Title:** Zeros of random analytic functions

**Abstract:** Consider the random entire function f(z)=a_0 + a_1 z/\sqrt{1!}
+a_2 z^2/\sqrt{2!} +... where a_n are independent and identically
distributed complex Gaussian random variables. This particular random
function has the remarkable property that its zeros have a
translation-invariant distribution on the plane. An analogous random
function on the disk is f(z)=a_0 + a_1 z + a_2 z^2 + ... whose zeros are
invariant in distribution under automorphisms of the unit disk. We shall
give an overview of some of very interesting properties of the zero sets
of these functions. The lecture should be accessible to anyone with some
familiarity with basic probability and basic complex analysis.