For more information about this meeting, contact Jason Morton.

Title: | Polyhedral combinatorics of conformal blocks and fusion algebras |

Seminar: | Applied Algebra 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 |