## EVENT DETAILS AND ABSTRACT

**Special Seminar**
**Title:** Complex zeros of random polynomials

**Speaker:** Steve Zelditch

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

A random polynomial is a polynomial $p_N(z) = \sum_{k=0}^N a_k z^k$ of one complex variable whose coefficients $a_k$ are random variables. Mark Kac introduced the simplest Gaussian random polynomial in the 50's, where the $a_k$ are i.i.d. N(0,1). Kac and Hammersley studied the zeros of $p_N(z)$ and found that the complex zeros cluster around the unit circle. My talk is devoted to the question: what in the Kac-Hammersley definition of of $a_k$ caused this strange distribution of zeros? Could we have designed the random variables $a_k$ to get any distribution of zeros?

**Date:** Monday, July 16, 2018

**Time:** 4:00pm

**Where:** Lunt 105

**Contact Person:** Antonio Auffinger

**Contact email:** tuca@northwestern.edu

**Contact Phone:** 847-491-5580

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