09:30 to 10:30 
Jurg Kramer 
On formal FourierJacobi expansions (Lecture ) It is a classical fact that Siegel modular forms possess socalled FourierJacobi expansions. The question then arises, given such an expansion, when does it originate from a Siegel modular form. In the complex setting, J. Bruinier and M. Raum gave a necessary and sufficient criterion when FourierJacobi expansions give rise to Siegel modular forms. In our talk we would like to revisit this problem however using the arithmetic compactifications of the moduli space of principally polarized abelian varieties established by G. Faltings and C.L. Chai. In particular, this will allow us to generalize the result of J. Bruinier and M. Raum to the arithmetic setting.



10:30 to 10:50 
 
Tea/cofee break 


10:50 to 11:50 
A. Raghuram 
Special values of RankinSelberg Lfunctions Günter Harder pioneered the study of Eisenstein cohomology on GL(2) as a tool to understand the special values of various Hecke Lfunctions. Over the last decade, Harder and I developed his earlier ideas to study Eisenstein cohomology on GL(N) over a totally real field and proved rationality results for the critical values of RankinSelberg Lfunctions. In continuation, I have worked on Eisenstein cohomology on GL(N) over a CM field. In this talk, I will report on some recent results of mine on the rationality properties of critical values of RankinSelberg Lfunctions for GL(n) x GL(m) over a CM field



11:50 to 12:00 
 
Break 


12:00 to 13:00 
Morten Risager 
Arithmetic statistics of modular symbols 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. These conjectures relate to the asymptotic growth of the first and second moments of the modular symbols, as well as the distribution of of modular symbols. We explain these conjectures and how they may be addressed using analytic properties of Eisenstein series twisted by modular symbols and how they can be extended to other situations.



13:00 to 14:15 
 
Lunch 


14:15 to 15:15 
Vincent Sécherre 
Supercuspidal representations of GL(n) over a padic field distinguished by a Galois involution Let p be an odd prime number and K/F be a quadratic extension of padic fields. Say that an irreducible complex representation of GL(n,K) is distinguished by GL(n,F) if its vector space carries a GL(n,F)invariant nonzero linear form. Any distinguished representation is isomorphic to the contragredient of its Gal(K/F)conjugate, but the converse is not true. We will explain how to canonically associate to any Gal(K/F)selfcontragredient cuspidal representation of GL(n,K) a finite tamely ramified extension T of F and a quadratic character of the multiplicative group of T, by using BushnellKutzko’s theory of types, and how to get a necessary and sufficient condition on this character for this cuspidal representation to be distinguished. Our approach is purely algebraic and local, and can be extended to representations with coefficients in a finite field of characteristic different from p. In that case, our necessary and sufficient condition still holds for supercuspidal representations. For cuspidal nonsupercuspidal representations, there are new phenomenons appearing.



15:45 to 16:45 
Sarah Dijols 
The Generalized Injectivity Conjecture The Generalized Injectivity Conjecture of CasselmanShahidi states that the unique irreducible generic subquotient of a (generic) standard module is necessarily a subrepresentation. It was proven for classical groups (SO(2n+1), Sp_{2n}, SO(2n)) by M.Hanzer in 2010. In my work, soon to be submitted, I am aiming at proving it for any quasisplit reductive group.
In this talk, I will describe some techniques more amenable to prove this conjecture for all quasisplit groups; I will also explain the architecture and key ideas going into the proof.


