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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2004-2005 MATHEMATICS COLLOQUIUM SERIES 02/07/05 Colloquium Dr. Michael Anshelevich   will speak on   Linearization Coefficients, Orthogonal Polynomials, and Free Probability           The linearization coefficients for a polynomial basis Pn are the coefficients in the expansion   Surprisingly, these coefficients turn out to be positive integers for a number of classical families. For the Hermite polynomials, they can be found explicitly using probability theory. For other families, such as the Chebyshev polynomials of the 2nd kind, one can use a different “free” probability theory. In this talk, we will outline the proof of this result, introducing all the necessary ingredients along the way.     Dr. Anshelevich received the PhD in Mathematics from UC Berkeley in May, 2000. He remained at Berkeley and at MSRI as a NSF postdoctoral fellow until 2002. Presently, he is an Assistant Professor at UC Riverside. His primary research interest is Operator Algebras and has components belonging to Combinatorics and Probability.                 DATE:        Monday, February 7, 2005                                 TIME:        3:30 – 4:30 P.M.                               PLACE:     Math and Physics Building, Room 233