On the coefficients of a bivariate rational function

School of Mathematics Colloquium
Thursday, September 15, 2011 - 11:05am for 1 hour (actually 50 minutes)
Skiles 006
Robin Pemantle – Math, University of Pennsylvania – pemantle@math.upenn.edu
Prasad Tetali
Problem: describe the asymptotic behavior of the coefficients a_{ij} of the Taylor series for 1/Q(x,y) where Q is a polynomial. This problem is the simplest of a number of such problems arising in analytic combinatorics whose answer was not until recently known. In joint work with J. van der Hoeven and T. DeVries, we give a solution that is completely effective and requires only assumptions that are met in the generic case. Symbolic algebraic computation and homotopy continuation tools are required for implementation.