Lorentz Center - The Geometric Langlands Program from 7 Jul 2008 through 11 Jul 2008
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    The Geometric Langlands Program
    from 7 Jul 2008 through 11 Jul 2008

 
The workshop will be a satellite activity of the fifth European Mathematical Congress (Amsterdam, 14-18 July 2008)
The workshop will be a satellite activity of the fifth European Mathematical
Congress  (Amsterdam, 14-18 July 2008). The workshop will be organized under
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 Netherlands and intends to promote the GLP as a 
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 
Fields Medal).
 
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 Witten have related the geometric Langlands 
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 
this area.
 
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:

Joergen Ellegaard Andersen (Univ. of Aarhus; CTQM)
Dima Arinkin (Univ. of Chicago)
Alexander Beilinson* (Univ. of Chicago)
David Ben-Zvi (UTexas, Austin)
Joseph Bernstein* (Tel Aviv University)
Roman Bezrukavnikov* (Univ. of Chicago)
Alexander Braverman* (Brown University)
Ron Donagi (Univ. of Pennsylvania)
Dennis Gaitsgory (Harvard University)
Victor Ginzburg (Univ. of Chicago)
Sergei Gukov (Caltech)
Michael Harris* (Univ. Paris 7)
Jochen Heinloth (Univ. of Amsterdam)
Anton Kapustin* (Caltech)
David Kazhdan* (Einstein Institute, Jerusalem)
Masaki Kashiwara* (RIMS)
Laurent Lafforgue* (IHES, Bures-sur-Yvette)
Vincent Lafforgue (ENS Paris)
Andrei Losev (ITP, Moscow)
Sergei Lysenko (Jussieu, Paris)
Ivan Mirkovic (Univ. Massachusetts)
David Morrison* (U. of California)
David Nadler (Univ. of Chicago)
Hiraku Nakajima* (U. of Kyoto)
Nikita Nekrasov* (IHES)
Raphael Rouquier* (Oxford)
Constantin Teleman* (UC Berkeley and Edinburgh)
Joerg Teschner (DESY)
Valerio Toledano Laredo (Northeastern University)
Kari Vilonen* (Northwestern University)
 



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