PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jason Morton.

Title:Polyhedral combinatorics of conformal blocks and fusion algebras
Seminar:Applied Algebra and Network Theory Seminar
Speaker:Chris Manon, U.C. Berkeley
Abstract Link:http://math.berkeley.edu/~manonc/Research.html
Abstract:
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
Date:04 / 03 / 2013
Time:04:40pm - 05:30pm