Special Seminar

Title: Complex zeros of random polynomials
Speaker: Steve Zelditch
Speaker Info: Northwestern University
Brief Description:
Special Note:

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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