## Distinguished Lecture Series

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.

*Previous speakers of the DLS include:* Peter Sarnak, Peter Schneider, Zhenghan Wang, Pierre Colmez, Etienne Ghys, Goro Shimura, Jean Bellissard, Andrei Suslin, Pierre Deligne, Michael Harris, Alexander Lubotzky, Shing-Tau Yau, Hillel Furstenberg, Robert R. Langlands, Clifford Taubes, Louis Nirenberg, Oded Schramm, Louis Nirenberg, I.M. Singer, Jesper Lutzen, L.H. Eliasson, Raoul Bott, Dennis Gaitsgory, Gilles Pisier, Gregg Zuckerman, Freydoon Shahidi, Alain Connes, Jöran Friberg, David Mumford, Sir Michael Atiyah, Jean-Michel Bismut, Jean-Pierre Serre, G. Tian, N. Sibony, C. Deninger, Peter Lax, and Nikolai Reshetikhin, Horng-Tzer Yau, Ken Ono, Leonid Polterovich, Barry Mazur, Grigori Margulis, Mario Bonk, Avi Wigderson, John Coates, Charles Fefferman, C. David Levermore, Shouwu Zhang.

**The DLS is currently supported by the Larry M. Wiener fund.**

## Past Lectures

Princeton University Visit: 06/06/2018 to 06/08/2018 |
University of Chicago Visit: 05/22/2018 to 05/24/2018 |
MIT Visit: 05/08/2018 to 05/10/2018 |

University of Sydney Visit: 05/30/2017 to 06/01/2017 |
College de France Visit: 05/09/2017 to 05/11/2017 |
Princeton University Visit: 04/04/2017 to 04/06/2017 |

Massachusetts Institute of Technology Visit: 01/24/2017 to 01/26/2017 |
Stanford University Visit: 11/14/2016 to 11/18/2016 |
Columbia University Visit: 05/17/2016 to 05/19/2016 |

Harvard University Visit: 04/25/2016 to 04/28/2016 |
Princeton University Visit: 05/19/2015 to 05/21/2015 |
Columbia University Visit: 02/17/2015 to 02/19/2015 |

Microsoft Research Visit: 11/03/2014 to 11/06/2014 |
Cambridge University Visit: 10/04/2014 to 10/10/2014 |
Duke University / UC Berkeley Visit: 05/19/2014 to 05/23/2014 |

IAS, Princeton Visit: 10/30/2013 to 11/06/2013 |
Texas A&M Visit: 10/22/2013 to 10/26/2013 |
Eötvös Loránd University Visit: 05/28/2013 to 05/30/2013 |

Rheinische Friedrich-Wilhelms-Universität Bonn Visit: 05/07/2013 to 05/09/2013 |
University of Strasbourg Visit: 04/03/2013 to 04/20/2013 |
Massachusetts Institute of Technology Visit: 01/24/2012 to 01/26/2012 |

Hebrew University Visit: 04/26/2011 to 04/28/2011 |

## Upcoming Lectures

### Jacob Lurie

#### Harvard University

**Visit:**

**Lectures:**

Lecture 1 (10/16): The Siegel Mass Formula and Weil's Conjecture

Lecture 2 (10/17): Weil's Conjecture for Function Fields

Lecture 3 (10/18): Weil's Conjecture via Factorization Homology

**Joint Abstract: **

Let L be a positive definite lattice. There are only finitely many positive definite lattices L' which are isomorphic to L modulo N for every N > 0: in fact, there is a formula for the number of such lattices, called the Smith-Minkowski-Siegel mass formula. In the first lecture, I'll review the Siegel mass formula and explain a reformulation (due to Tamagawa and Weil) in terms of the volumes of certain adelic groups. This reformulation led Weil to conjecture a generalization of the mass formula, which applies to any (simply connected) semisimple algebraic group G over any global field K. In the second lecture, I'll discuss the meaning of this conjecture in the case where K is a function field (that is, a finite extension of F_p(x), for some prime number p), and explain how it can be reformulated as a statement about the cohomology of certain moduli spaces. In the third lecture, I'll discuss recent joint work with Dennis Gaitsgory, applying ideas from algebraic topology to compute the relevant cohomology groups and thereby obtain a proof of Weil's conjecture in the function field case.

**Poster:** LURIE.pdf