Modular forms, p-adic L-functions and Selmer groups
July 7-13, 2013 - NIO (Oriahovitza), Bulgaria
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:
Vanishing of L-functions and rank of Selmer groups for rational elliptic curves (a mini-course by Skinner and Urban),
the study of the p-adic L-functions of symmetric and tensor products
of modular forms,
the use of generalized modular symbols for the constructions of
p-adic L-functions of automorphic forms,
the construction of p-adic L-functions on Eigenvarieties,
L-invariants and p-adic Hodge theory,
deformation of Galois representations and Selmer groups.
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:
