The Geometric Langlands Program

7 - 11 July 2008

Venue: Lorentz Center@Oort

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The workshop will be a satellite activity of the fifth European MathematicalCongress  (Amsterdam, 14-18 July 2008). The workshop will be organized underthe auspices of the research cluster “Geometry and Quantum Theory''. We intend to bring together leading mathematicians working on the GeometricLanglands 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 Galoisrepresentations, 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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    Gert Heckman  

    Eduard Looijenga  

    Eric Opdam  

    Edward Frenkel, University of California, Berkeley  


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