Friday, January 9, 2009
3:30 pm, MC 5158

Kevin Purbhoo
University of Waterloo

Jeu de Taquin and Wronskians of polynomials

Jeu de taquin was first introduced by Schutzenberger in the 1970s, and is now considered a fundamental construction in the combinatorics of Young tableaux. However, from the point of view of other branches of mathematics which use Young tableaux, (e.g. geometry, representation theory), it is not so clear why jeu de taquin is a natural operation. Surprisingly, jeu de taquin arises in a very natural way in studying the following problem:
Let g(z) be a polynomial. What can we say about the set of d-tuples of polynomials whose Wronskian equals g(z)?
I will talk about some of the history of this problem, and explain where jeu de taquin fits in.