### 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.