Number theory seminar

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Spring Semester 2017

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Date / Time Speaker Title Location
24 February 2017
14:15-15:15
Prof. Dr. François Charles
Université Paris-Sud
An arithmetic Bertini theorem  HG G 43 
Abstract: The Bertini irreducibility theorem states that, over an infinite field, a general hyperplane section of projective variety that is irreducible of dimension at least 2 remain irreducible. Over a finite field, this statement does not hold, but we can salvage it by replacing hyperplane sections by hypersurfaces of larger degree (joint with Poonen). We will explain how to prove the arithmetic version of this result.
10 March 2017
14:15-15:15
Prof. Dr. Solomon Friedberg
Boston College
New integrals for tensor product L-functions  HG G 43 
Abstract: After giving necessary background, I will discuss new integrals representing tensor product L-functions of classical groups with general linear groups. These require new ingredients from the representation theory of p-adic groups (new kinds of unique models). The integrals also work for covering groups. Though there is still more work to be done, these integrals remove the main obstruction to proving the existence of endoscopic lifts for all automorphic representations without using the trace formula. This is joint work with Cai, Ginzburg and Kaplan.
31 March 2017
14:15-15:15
Prof. Dr. Yiannis Petridis
University College London
Arithmetic Statistics of modular symbols  HG G 43 
Abstract: Mazur, Rubin, and Stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve L-functions. Two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols. In joint work with Morten S. Risager we prove these on average using analytic properties of Eisenstein series twisted with modular symbols. We also prove another conjecture predicting the Gaussian distribution of normalized modular symbols ordered according to the size of the denominator of the cusps.
7 April 2017
14:15-15:15
Dr. James Borger
ANU
Witt vectors, lambda-rings, and positivity  HG G 43 
Abstract: The concepts of big Witt vectors and lambda-rings extend naturally from the category of rings to that of semirings. This implies, for example, that there are natural positivity structures on Witt vectors of rings which themselves have positivity structures---most importantly the integers and the real numbers. I'll explain this and make some enticing possible connections to the philosophy of the field with one element and Deninger's hypothetical arithmetic dynamical systems.
12 May 2017
14:15-15:15
Prof. Dr. Abhishek Saha
Bristol University
Title T.B.A. HG G 43 
* 18 May 2017
11:15-12:15
Prof. Dr. Youness Lamzouri
York University
Title T.B.A. HG G 43 
26 May 2017
14:15-15:15
Tiago Fonseca
Université Paris-Sud
Title T.B.A. HG G 43 
* 2 June 2017
Number Theory Days in Lausanne

Archive: SS 17  AS 16  SS 16  AS 15  SS 15  AS 14  SS 14  AS 13  SS 13  AS 12  SS 12  AS 11  SS 11  AS 10  SS 10  AS 09 

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Wed Apr 26 21:00:04 CEST 2017
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