Date: | January 24 (Sat)-26 (Mon), 2015 |

Venue: | Graduate School of Mathematical Sciences, The University of Tokyo, Japan [ Access ] |

January 24 (Sat) | 13:00-14:00, Room 126Peter Trapa"Unitary representations of reductive Lie groups I" |

14:30-15:30, Room 126Raul Gomez"The Tor and Ext functors for smooth representations of real algebraic groups" | |

16:30-17:30, Room 126Benjamin Harris"The Geometry of Tempered Characters" | |

January 25 (Sun) | 9:00-10:00, Room 126Raul Gomez"Generalized and degenerate Whittaker models associated to nilpotent orbits" |

10:30-11:30, Room 126Benjamin Harris"The Geometry of Harmonic Analysis" | |

12:00-13:00, Room 126Peter Trapa"Unitary representations of reductive Lie groups II" | |

January 26 (Mon) | 9:30-10:30, Room 122Benjamin Harris"The Geometry of Nontempered Characters" |

11:00-12:00, Room 122Raul Gomez"Local Theta lifting of generalized Whittaker models" | |

12:30-13:30, Room 128Peter Trapa"Unitary representations of reductive Lie groups III" | |

Speaker |
Benjamin Harris (Oklahoma State University) [ pdf ] |

Title | The Geometry of Tempered Characters |

Abstract | In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R). |

Title | The Geometry of Harmonic Analysis |

Abstract | In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result. |

Title | The Geometry of Nontempered Characters |

Abstract | In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures. |

Speaker |
Peter Trapa (University of Utah) [ pdf ] |

Title | Unitary representations of reductive Lie groups I, II, III |

Abstract | Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form. This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan. |

Speaker |
Raul Gomez (Cornel University) [ pdf ] |

Title | 1. The Tor and Ext functors for smooth representations of real algebraic groups |

Abstract | Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh. |

Title | 2. Generalized and degenerate Whittaker models associated to nilpotent orbits |

Abstract | In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications. This is joint work with Dmitry Gourevitch and Siddhartha Sahi. |

Title | 3. Local Theta lifting of generalized Whittaker models |

Abstract | In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu. |

Organizers: T. Kobayashi, T. Kubo, H. Matumoto, H. Sekiguchi |