# MIT Yakov Varshavsky Lecture Series

algebraic geometry number theory representation theory

Audience: | Researchers in the topic |

Seminar series time: | Every other Friday 14:00-16:00 in your time zone, UTC |

Organizer: | Roman Bezrukavnikov* |

*contact for this listing |

This a series of biweekly lectures given by Yakov Varshavsky.

Please note the schedule change on October 4.

For directions to MIT building 2, please go to whereis.mit.edu/?go=2

--

Series abstract:

Harmonic analysis on reductive p-adic groups (such as the group GL(n,Q_p) of invertible matrices with entries in the p-adic field) is a central part of Langlands program.

It follows from general topological properties that characters of irreducible representations form a topological basis in the space of invariant generalized functions on the group. Langlands' theory of endoscopy studies subtle properties of these characters stemming from algebro-geometric and arithmetic nature of the group. In particular, Langlands conjectured that some specific linear combinations of characters satisfy the so called E-stability property, which relates the values of the class function on two elements conjugate over the algebraic closure of the p-adic field.

After a general introduction to this circle of ideas I will present an approach to these conjecture based on the idea that the above linear combinations should come from geometry : they are expected to be closely related to perverse equivariant sheaves on the loop group. While perverse sheaves have become a standard tool in geometric representation theory, the present setting involves "truly infinite dimensional" spaces, the definition and basic properties of such sheaves in this setting were only worked out recently.

The above picture will be illustrated by specific results covering two particular cases: cuspidal Deligne-Lusztig representations and unipotent representations of GL(n,F). The results are partly motivated by conjectures proposed by Lusztig.

Most original results to be presented in the lectures are from joint works with Bezrukavnikov, Bouthier and Kazhdan.

Your time | Speaker | Title | |||
---|---|---|---|---|---|

Fri | Oct 25 | 14:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups | |

Fri | Nov 08 | 15:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups | |

Fri | Nov 22 | 15:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups | |

Fri | Dec 06 | 15:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups |

Your time | Speaker | Title | |||
---|---|---|---|---|---|

Fri | Oct 04 | 14:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups | |

Fri | Sep 27 | 14:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups | |

Fri | Sep 13 | 14:00 | Yakov Varshavsky | Harmonic analysis on p-adic groups and sheaves on loop groups |