# NTS/Abstracts/Fall2010

## Contents

## Jordan Ellenberg, UW Madison

Title: Expander graphs, gonality, and Galois representations |

Abstract: TBA |

## Shuichiro Takeda, Purdue

Title: On the regularized Siegel-Weil formula for the second terms and
non-vanishing of theta lifts from orthogonal groups |

Abstract: In this talk, we will discuss (a certain form of) the Siegel-Weil formula for the second terms (the weak second term identity). If time permits, we will give an application of the Siegel-Weil formula to non-vanishing problems of theta lifts. (This is a joint with W. Gan.) |

## Xinyi Yuan

Title |

Abstract. |

## Jared Weinstein, IAS

Title: Semistable reduction of modular curves |

Abstract. |

## David Zywna, U Penn

Title |

Abstract. |

## Soroosh Yazdani, UBC and SFU

Title |

Abstract. |

## Zhiwei Yun, MIT

Title: From automorphic forms to Kloosterman sheaves (joint work with J.Heinloth and B-C.Ngo) |

Abstract: Classical Kloosterman sheaves are rank n local systems on the punctured line (over a finite field) which incarnate Kloosterman sums in a geometric way. The arithmetic properties of the Kloosterman sums (such as estimate of absolute values and distribution of angles) can be deduced from geometric properties of these sheaves. In this talk, we will construct generalized Kloosterman local systems with an arbitrary reductive structure group using the geometric Langlands correspondence. They provide new examples of exponential sums with nice arithmetic properties. In particular, we will see exponential sums whose equidistribution laws are controlled by exceptional groups E_7,E_8,F_4 and G_2. |

## Samit Dasgupta, UC Santa Cruz

Title |

Abstract. |

## Jay Pottharst, Boston University

Title: Iwasawa theory at nonordinary primes |

Abstract. |

## Toby Gee, Northwestern

Title |

Abstract. |

## Organizer contact information

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