Mathematics Department EIGHTH RAMANUJAN^{*} COLLOQUIUM by Professor Peter Paule ^{**} Director Research Institute on Symbolic Computation Johannes Kepler University, Linz, AUSTRIA on ANDREWS, RAMANUJAN, AND COMPUTER ALGEBRA
Abstract: The thread of the talk is made from various mathematical ideas which, to my pleasure, George Andrews was sharing with me already in statu nascendi. The first part of the talk is devoted to aspects of partition analysis, invented by MacMahon more than a hundred years ago, and brought back to the stage by Andrews. Partition analysis is a method to deal with systems of linear Diophantine constraints over the non-negative integers and thus providing connections to many areas in discrete mathematics, including discrete geometry. Computer algebra experiments carried out with Omega, a computer algebra package implemented by Axel Riese in cooperation with Andrews and the speaker, led to a new combinatorial construction of quotients of Dedekind eta functions. This work in turn stimulated new algorithmic developments by Silviu Radu to manipulate modular forms and functions, and to prove related congruences arising in additive number theory. The talk gives a general overview with numerous examples, many of them related, directly or indirectly, to Srinivasa Ramanujan.
^{**} ABOUT THE SPEAKER: Peter Paule is Professor of Mathematics and Director of the Research Institute for Symbolic Computation (RISC) at the Johannes Kepler University, Linz, Austria. His main research interests are computer algebra and algorithmic mathematics, together with connections to combinatorics, special functions, number theory, and other related fields. He is on the editorial boards for the Journal of Symbolic Computation and The Ramanujan Journal, and is Managing Editor of Annals of Combinatorics. He is Editor-in-Chief of the Springer book series Texts and Monographs in Symbolic Computation. In January 2014, he was elected Fellow of the American Mathematical Society. Ramanujan Colloquium * University of Florida * Mathematics |