Outline
The theory of Galois representations is a flourishing area of activity in the
landscape of presentday arithmetic. Since Wiles' proof of Fermat's
Last Theorem, the theory of automorphic forms has played an especially important role,
via Langlands program and the connections it entails. There has also been a
convergence
of significant themes arising from nonabelian class field theory.
The symposium will present an overview of current developments,
focussing on some of the significant advances since the
LMS Durham Symposium of 2004 such as:

The proof of Serre's conjecture and most cases of the FontaineMazur conjecture for GL(2);

Higherrank generalisations of modularity theorems,
with applications such as the proof of the SatoTate conjecture;

The development of the padic Langlands program and its applications
to the classical Langlands program;

The proof of the fundamental lemma on orbital integrals and its applications to
Langlands functoriality and the cohomology of Shimura varieties.
There will be five onehour lectures per day, some of which
will constitute short courses of 35 lectures. A tentative list
of these is:
 The padic Langlands correspondence
 Vector bundles and padic Hodge theory
 The fundamental lemma and trace formulas
 Automorphy of Galois representations
 Fundamental groups
In addition to the main themes, there will be
lectures on related topics of critical interest, such as
padic Hodge theory, special values of Lfunctions,
and nonabelian Iwasawa theory.
The aim of the lectures will be to provide to young researchers
a bird'seye view of the ideas and techniques, and to the experienced researchers
the opportunity to learn of exciting new developments in neighbouring areas and
to build bridges for collaboration.
Organising Committee:
Fred Diamond (King's College London), Payman Kassaei (King's College London), Minhyong Kim (University College London)
