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Mathematics Colloquium


Date:  Tuesday, December 07, 2010

Title:  Zeros of random functions on complex manifolds

Abstract:  How are the zeros of typical polynomials or entire functions on C^n distributed? How are typical divisors of ample line bundles distributed? The answers depend on what is meant by "typical." We consider various random ensembles of polynomials, and more generally holomorphic sections, and study the properties of their zero currrents and of their simultaneous zero sets. How much clustering occurs? How likely are the "typical" distributions? The answers to these and other questions depend on the geometry of the corresponding Bergman kernels. We shall describe the asymptotic properties of Bergman kernels for linear systems of increasing degree and their impact on the distributions of zeros.

Speaker:  Bernie Shiffman
Institution:  Johns Hopkins Univ


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