Title: Symbolic computation, combinatorics, and modular forms
Speaker: Peter Paule
Abstract: The common thread of the talk concerns computational interpretations
(resp. refinements) of mathematical theorems and methods in the fields
of combinatorics and additive number theory. The starting point is an
algorithmic revitalization (joint with George Andrews and Axel Riese)
of partition analysis, a combinatorial method invented by MacMahon more
than a hundred years ago. Corresponding computer algebra software led
to the discovery of a new combinatorial construction of modular forms,
which in turn gave rise to new number-theoretic congruences satisfied
by partition numbers. Part two of the talk describes new algorithmic
developments (by Cristian-Silviu Radu and also in joint work with Radu)
in the theory of modular forms that allow new proof methods for related
q-series identities, including a new unified proving frame for the
celebrated families of partition congruences modulo powers of 5, 7,
and 11 discovered by Ramanujan.