Number Theory Days in Lille

Session

Galois representations and modular forms

9 juil. 2019, 09:00

Salle de réunion (Université de Lille)

45. Applications of the orbit method to the analysis of automorphic forms

Paul Nelson (ETH Zurich)

09/07/2019 09:45

I will discuss joint work with Akshay Venkatesh in which we use microlocalized test vectors (inspired by the orbit method) and Ratner theory to study mean values of L-functions on Gross--Prasad pairs. I will also indicate some further applications of these methods, such as to the quantum variance problem for Hecke--Maass eigenforms.

55. Birch and Swinnerton-Dyer Formula for modular forms of arbitrary weight in the cases of analytic ranks 0 and 1

Dimitar Jetchev (EPFL)

09/07/2019 11:00

In this talk, I will report on recent results on the computation of the p-part of the leading term of the L-function of a modular form of arbitrary weight at the central point in the cases when the order of vanishing is at most one. Unlike the classical case of weight 2 modular forms, qualitatively different arguments are needed in the higher-weight case. After explaining the difference, I...

56. On a conjecture of Gross and explicit formula for Gross-Stark units

Mahesh Kakde (King's College London)

09/07/2019 14:00

In this talk I will report on my joint work in progress with Samit Dasgupta on the tower of fields conjecture first formulated by Gross. This proves a conjecture of Dasgupta on explicit p-adic analytic formulae for Gross-Stark units. These units, when considered for all primes of a totally real number field F, generate the maximal abelian CM extension of F and therefore our work can be...

52. Overconvergent cohomology and automorphic p-adic L-functions

Daniel Barrera (Universidad de Santiago de Chile)

09/07/2019 15:30

p-adic L-functions attached to automorphic representations and p-adic families of them, provide powerful tools to attack important problems such as Birch-Swinnerton-Dyer and Bloch-Kato conjetures. However, they are hard to construct and in fact beyond the case GL(2) the theory is poorly understood.

In this talk I will describe an approach based on the study of the overconvergent cohomology...

46. Image of two-dimensional pseudorepresentations

Jaclyn Lang (Université Paris 13)

11/07/2019 09:45

There is a general philosophy that the image of a Galois representation should be as large as possible, subject to its symmetries. This can be seen in Serre's open image theorem for non-CM elliptic curves, Ribet and Momose's work on Galois representations attached to modular forms, and recent work of the speak and Conti-Iovita-Tilouine on Galois representations attached to p-adic families of...