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The Geometric Langlands Program
The workshop will be a satellite activity of the fifth European Mathematical
the auspices of the research cluster “Geometry and Quantum Theory''.
We intend to bring together leading mathematicians working on the Geometric
Langlands Program. The GLP has deep connections with Number Theory,
Algebraic Geometry and with subjects from mathematical physics such as
Quantization and Conformal Field Theory. Internationally the subject has quickly
become a major theme bridging between these fields. The proposed workshop
brings together various research communities in pure mathematics and
mathematical physics in the
unifying research theme.
The Langlands Program has emerged in the late 1960s in the form of a series of
far-reaching conjectures tying together seemingly unrelated objects in number
theory, algebraic geometry, and the theory of automorphic forms (such as Galois
representations, motives, and automorphic forms). In the past decade there have
been exciting new developments and breakthrough discoveries in this area.
The “Geometric Langlands Program'' is a very prominent case in point. The
Langlands conjectures may be formulated geometrically for the field of functions
of a curve over a finite field. This insight is at the basis of Drinfeld's proof of the
Langlands conjecture for GL(2) in the function field case. The approach by
Drinfeld was extended by Laurent Lafforgue, who proved the Langlands
conjecture for GL(n) in the function field case (a feat that earned him in 2002 a
Based on Drinfeld's geometric appraoch to the Langlands conjectures Drinfeld
and Laumon formulated a geometric variant of the Langlands correspondence
which makes sense for the function field of a curve X defined over an arbitrary
field. It relates Hecke eigensheaves on the moduli stack of principal G-bundles
over X and equivariant local systems for the Langlands dual group of G.
In the workshop we intend to concentrate on recent developments in the
Geometric Langlands Program. Many of these developments are interrelated and
cross fertilize each other. There are deep connections between the Langlands
Program and Quantum Field Theory and Statistical Mechanics. In a series of
recent works, Gukov, Kapustin and
correspondence to S-duality in four-dimensional supersymmetric Yang-Mills
theory. In addition, the Langlands duality has been related to the IM/ODE
correspondence in integrable models. This opens new directions of research in
We also want to make this workshop worthwhile for an audience of young and
beginning researchers and in order to have this category of participants better
prepared, we intend to organize a seminar shortly before the workshop.
Current list of invited participants: