# Mathematics Colloquia and Seminars

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### BRST reduction of the chiral Hecke algebra

**Algebra & Discrete Mathematics**

Speaker: | Ilya Shapiro, UC Davis |

Location: | 1147 MSB |

Start time: | Fri, May 18 2007, 3:10PM |

The chiral Hecke algebra, introduced by Beilinson and Drinfeld, is a geometrically defined vertex algebra with many wonderful applications. In particular, it is conjectured to play a role in the affine version of the Beilinson-Bernstein localization theorem at a below critical integral level. I will describe its BRST reduction, which is a vertex algebra. The computation is for the most part geometric due to the relation between the BRST reduction and the de Rham cohomology, the latter can be computed using a theorem of Mirkovic and Vilonen.