"Having a ball with Young tableaux"

The century old Young tableaux are beloved
by combinatorialists, while tolerated by
geometers and representation theorists.

Allen Knutson, Ezra Miller and I observed that
they index a set of n-dimensional tetrahedra that
naturally glue together. While many spaces arise
by such gluings, in this case our simplicial complex
has the topology of an n-dimensional ball!
See a picture at

http://www.math.umn.edu/~ayong/vexcomplex.jpg

I'll explain why this is true, surprising, and
explain some applications. Time permitting, I'll
describe a general context of "tableaux complexes"
that we developed to understand this phenomenon.

This is based on math.CO/0510487.