DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Co-organizers:

Andrew Baxter, Rutgers University, baxter{at} math [dot] rutgers [dot] edu

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Advanced Applications of the Holonomic Systems Approach

Speaker: Christoph Koutschan, Tulane University

Date: Thursday, December 3, 2009 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Since the holonomic systems approach has been proposed by D. Zeilberger in the early 1990s, it has received a lot of attention and has proved to be useful in various applications. In our talk we want to present results of our PhD thesis which has close connections to this approach. The core of our work is a new, very powerful Mathematica implementation of the related algorithms (noncommutative Groebner bases, closure properties for multivariate holonomic functions, creative telescoping for such functions in order to solve integration and summation problems, some extensions to deal with non-holonomic functions). This implementation then served for solving several nontrivial problems, including an open conjecture from combinatorics and questions that arose in numerical simulations using finite element methods.