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Math Colloq: Prof. Van Vu
Mon, Mar 29, 2010
Thomas Lord Department of Computer Science
Conferences, Lectures, & Seminars
Speaker: Prof. Van Vu (Rutgers University)Host: Center for Applied Mathematical Sciences ( http://www.usc.edu/dept/LAS/CAMS/Colloquia/3-29-2010.html )Talk Title:
Inverse Littlewood-Offord theory, Smooth Analysis and the Circular LawAbstract:
A corner stone of the theory of random matrices is Wigner's semi-circle law, obtained in the 1950s, which asserts that (after a proper normalization) the limiting distribution of the spectra of a random hermitian matrix with iid (upper diagonal) entries follows the semi-circle law. The non-hermitian case is the famous Circular Law Conjecture, which asserts that (after a proper
normalization) the limiting distribution of the spectra of a random matrix with iid entries is uniform in the unit circle.Despite several partial results (Ginibre-Mehta, Girko, Bai, Edelman, Gotze-Tykhomirov, Pan-Zhu etc) the conjecture remained open for more than 50 years. In 2008, T. Tao and I confirmed the conjecture in full generality. I am going to give an overview of this proof, which relies on rather surprising connections between various fields: combinatorics, probability and, particularly, theoretical computer science.
Location: Kaprielian Hall (KAP) - 414
Audiences: Everyone Is Invited
Contact: CS Front Desk
