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Spring Semester 2017
Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.
Date / Time  Speaker  Title  Location  

24 February 2017 14:1515:15 
Prof. Dr. François Charles Université ParisSud 
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 14:1515:15 
Prof. Dr. Solomon Friedberg Boston College 
New integrals for tensor product Lfunctions  HG G 43  
Abstract: After giving necessary background, I will discuss new integrals representing tensor product Lfunctions of classical groups with general linear groups. These require new ingredients from the representation theory of padic 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 14:1515:15 
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 Lfunctions. 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 14:1515:15 
Dr. James Borger ANU 
Witt vectors, lambdarings, and positivity  HG G 43  
Abstract: The concepts of big Witt vectors and lambdarings 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 structuresmost 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.  
*
14 April 2017 
No seminar (Easter Friday; vacations)  
*
21 April 2017 14:1515:15 
No seminar, vacations  
*
5 May 2017 
No seminar: Grothendieck Seminar at FIM  
12 May 2017 14:1515:15 
Prof. Dr. Abhishek Saha Bristol University 
Integral representation and critical Lvalues for the standard Lfunction of a Siegel modular form  HG G 43  
Abstract: I will talk about some of my recent work with Pitale and Schmidt where we prove an explicit pullback formula that gives an integral representation for the twisted standard Lfunction for a holomorphic vectorvalued Siegel cusp form of degree n and arbitrary level. In contrast to all previously proved pullback formulas in this situation, our formula involves only scalarvalued functions despite being applicable to Lfunctions of vectorvalued Siegel cusp forms. Further, by specializing our integral representation to the case n = 2, we prove an algebraicity result for the critical Lvalues in that case (generalizing previously proved criticalvalue results for the full level case).  
*
18 May 2017 11:1512:15 
Prof. Dr. Youness Lamzouri York University 
Large sums of Hecke eigenvalues of holomorphic cusp forms  HG G 43  
Abstract: Let $f$ be a Hecke cusp form of weight $k$ for the full modular group, and let $\lambda_f(n)\}_{n\geq 1}$ be the sequence of its normalized Fourier coefficients. In this talk, we will present recent results on the order of magnitude of the short sums $S_f(x)=\sum_{n\leq x} \lambda_f(n)$ (where $x$ varies in terms of $k$), as well as applications to the first negative Hecke eigenvalue. To explore these sums, we shall introduce a probabilistic random model for $S_f(x)$, and compare this sum to the sum of the divisor function $\tau(n)$ over smooth (or friable) numbers. Our results are $GL_2$ analogues of work of Granville and Soundararajan on character sums, and could also be generalized to other families of automorphic forms.  
26 May 2017 14:1515:15 
Tiago Fonseca Université ParisSud 
Higher Ramanujan equations and periods of abelian varieties  HG G 43  
Abstract: The Ramanujan equations are some algebraic differential equations satisfied by the classical Eisenstein series E_2, E_4, E_6. These equations play a pivotal role in the proof of Nesterenko's celebrated theorem on the algebraic independence of values of Eisenstein series, which gives in particular a lower bound on the transcendence degree of fields of periods of elliptic curves. Motivated by the problem of extending the methods of Nesterenko to other settings, we shall explain in this talk how to generalize Ramanujan's equations to higher dimensions via a geometric approach, and how the values of a particular solution of these equations relate with periods of abelian varieties.  
*
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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