# Synopsis and Organizers

**Geometric methods in representation theory and number theory**

The Master Lectures by Professor Schmid will center around Lie groups and arithmetic. The Master Lectures themselves will cover the Peter-Weyl theorem, the Weyl character formula, and analogues for noncompact Lie groups. A main theme will be the decomposition of L^{2}(G/H), where H is a subgroup of a reductive Lie group G. In particular interesting nontempered representations occur, and are important in understanding theunitary dual of G -- a topic which several of the workshop lectures will be devoted to. The most important applications are for arithmetic subgroups H; there will also be several lectures on applications of representation theory to automorphic forms, L-functions, and Voronoi summation formulas. In particular the lectures will cover the use of automorphic distributions in analytic number theory, such as in deriving subconvexity estimates for GL(3) L-functions and cancellation in arithmetically twisted sums.

**Organizers**

Name | University |
---|---|

Organizer | |

Wilfried Schmid | Harvard University |

Shouwu Zhang | Princeton University |

Co-organizers | |

Dragan Milicic | University of Utah |

Stephen D. Miller | Rutgers, The State University of New Jersey |

Ye Tian | Chinese Academy Of Sciences |

Xinyi Yuan | Princeton University |