Monday March 1, 2004

Speaker: Igor Pak (MIT)

Title: The nature of partition bijections

Abstract: The study of partition identities has a long history going back to Euler, with applications ranging from Analysis to Number Theory, from Enumerative Combinatorics to Probability. Partition bijections is a combinatorial approach which often gives the shortest and the most elegant proofs of these identities. These bijections are then often used to generalize the identities, find "hidden symmetries", etc. But to what extent can we use these bijections? Do they always, or at least often exist, and how do you find them? Why is it that some bijections seem more important than others, and what is the underlying structure behind the "important bijections"? I will try to cover a whole range of partition bijections and touch upon these questions. The talk assumes no background whatsoever, and hopefully will be somewhat entertaining.