# Meeting Details

Title: Polyhedral combinatorics of conformal blocks and fusion algebras Applied Algebra and Network Theory Seminar Chris Manon, U.C. Berkeley http://math.berkeley.edu/~manonc/Research.html For a simple complex Lie algebra $\mathfrak{g}$ and a non-negative integer $L$, the fusion algebra or Verlinde algebra $\mathcal{F}_L(\mathfrak{g})$ is an elegant finite dimensional algebra which encodes the dimensions of the spaces of partition functions for the Wess-Zumino-Witten model of conformal field theory. When $\mathfrak{g} = sl_m(\\mathbb{C})$, this algebra also makes an appearance as the small quantum cohomology ring of the Grassmannian variety $Gr_m(\mathbb{C}^{m+L}).$ We will describe what we have been calling a polyhedral presentation of this algebra for $sl_2(\mathbb{C})$ and $sl_3(\mathbb{C})$, and how such a presentation is given by combinatorics related to moduli spaces of vector bundles of rank $2$ and rank $3$. We will further explain how such a presentation for $sl_m(\mathbb{C})$ with $m > 3$ would be related to questions about moduli of higher rank vector bundles. Time permitting, we will also give some remarks on how these constructions are related to phylogenetics.

### Room Reservation Information

Room Number: MB106 04 / 03 / 2013 04:40pm - 05:30pm