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# Robin PEMANTLE : Analytic Combinatorics in Several Variables Subtitle: estimating coefficients of multivariate rational power series

The analytic framework for estimating coefficients of a generating function is the same in many variables as in one variable: evaluate Cauchy's integral by manipulating the contour into a "standard" position. That being said, the geometry when dealing with several complex variables can be much more complicated. This talk, drawing on the recent book (with Mark Wilson) of the same title, surveys analytic methods for extracting asymptotics from multivariate generating functions. I will try to give an idea of the main pieces of the puzzle. In particular, I will try to explain in pictures the roles of Morse theory, complex algebraic geometry and hyperbolicity in the asymptotic evaluation of integrals.

**Category**: Probability**Duration**: 01:14:48**Date**: March 26, 2014 at 11:55 AM**Views**: 101-
**Tags:**seminar, Probability Seminar

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