The glue between Young tableaux
Allen Knutson (Berkeley)

Semistandard Young tableaux have been studied for a century in combinatorics, representation theory, and the algebraic geometry of determinantal varieties. I'll show how Anders Buch's generalization, "set-valued tableaux", serve as a sort of glue between ordinary tableaux, in that all tableaux fit into a simplicial complex with Buch's tableaux corresponding to lower-dimensional faces. The evidence that this is a combinatorially natural thing to do is that the simplicial complex is homeomorphic to a ball.
In fact some Gröbner bases of determinantal varieties handed us this combinatorial structure. I'll give a hint of that connection if time permits.

This work is joint with Ezra Miller (University of Minnesota) and Alex Yong (University of Illinois at Urbana-Champaign).