On the coefficients of a bivariate rational function

School of Mathematics Colloquium
Thursday, September 15, 2011 - 11:05
1 hour (actually 50 minutes)
Skiles 006
Math, University of Pennsylvania
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.