Modular forms, p-adic L-functions and Selmer groups

July 7-13, 2013 - NIO (Oriahovitza), Bulgaria

Organizers: Mladen Dimitrov, Ivan Horozov, Jacques Tilouine and Eric Urban

Program of the Opening Session (July 8th, 2013 - FMI, room 325, University of Sofia)
Program of the conference (July 9-12, 2013 - NIO, Oriahovitza)
List of Participants

Lecture notes:

John Bergdall (Brandeis University, USA) Parabolizations over families of trianguline representations
Tobias Berger (University of Sheffield, UK) An analogue of Shintani's theta lift for imaginary quadratic fields
Gebhard Böckle (Heidelberg University, Germany) Images of p-adic Galois representations
Ehud de Shalit (Hebrew University, Israel) L-invariants of p-adically uniformized varieties
Adam Gamzon (Hebrew University, Israel) Unobstructed Hilbert modular deformation problems
Ralph Greenberg (University of Washington, USA) Iwasawa theory for Artin representations
Robert Harron (University of Wisconsin-Madison, USA) Computing Hida families using overconvergent modular symbols
Haruzo Hida (University of California, Los Angeles, USA) Arithmetic of Weil numbers and Hecke fields
Fabian Januszewski (Karlsruhe Institute of Technology, Germany) On the non-vanishing of periods for GL(n) x GL(n-1)
Dimitar Jetchev (EPFL, Switzerland) Euler Systems from CM cycles for Unitary Shimura Varieties and the Gross-Prasad Conjectures
Andrei Jorza (Caltech, USA) L-invariants for symmetric powers of Hilbert modular forms
Matteo Longo (University of Padova, Italy) A refined Beilinson-Bloch Conjecture for motives of modular forms
Giovanni Rosso (University Paris 13, France, and KU Leuven, Belgium) Trivial zero for the symmetric square of an elliptic curve over a totally real field
Victor Rotger (Universitat Politecnica de Catalunya, Spain) Stark-Heegner points and iterated p-adic integrals
Christopher Skinner (Princeton University, USA) P-adic numbers and their uses in number theory
Jacques Tilouine (University Paris 13, France) Big image of automorphic Galois representations and congruence ideals
Eric Urban (Columbia University, USA) Vanishing of L-functions and rank of Selmer groups for rational elliptic curves
Jeanine Van Order (EPFL, Switzerland) Galois averages of automorphic L-functions
Sarah Zerbes (University College London, UK) Euler systems for Rankin-Selberg convolutions

Conference description:

The tight links between special values of L-functions of motives and their Galois cohomology have been progressively brought to light during the 20th century. Fundamental conjectures have been formulated, like the famous Birch and Swinnerton-Dyer conjecture for elliptic curves and more recently the Bloch and Kato conjecture for a general motive. The study of these questions has contributed to the development of the Iwasawa theory and of the theory of p-adic deformation of Galois representations and modular forms. In particular, in order to formulate p-adic analogues of these conjectures (Iwasawa and Greenberg Main Conjectures), it has been necessary to construct p-adic L-functions for motives and their p-adic deformations, as well as to introduce the corresponding Galois cohomology objects (Selmer groups and complexes). Important progress on various aspects of these questions has been achieved using results from Langlands' functoriality, the cohomology of Shimura varieties and the theory of p-adic families of modular forms (Hida, Coleman...) and Galois representations (Mazur...).

This conference aims at gathering internationally renowned experts who will present the main topics of the conference, in the form of lectures and mini-courses, to participating graduate students and postdocs, in the hope of creating scientific connections that may lead to future collaborations.

The topics of the conference include:

Practical Information:

Participants are expected to arrive on Sunday July 7th, at Sofia International Airport. The opening session, consisting of three colloquium-type lectures, will be held at the The Faculty of Mathematics and Informatics of the University of Sofia on Monday July 8th. The conference will take place in the National Institute for Education (NIO), which is part of the Minu Balkanski Foundation, located in the Bulgarian village of Oriahovitza (250km from Sofia), where the participants will be taken by bus on Monday afternoon. The last talks will be on Friday afternoon and there will be an organized transfer back to Sofia early on Saturday July 13th.

The conference is sponsored by: