Home /  Geometric Aspects of the Langlands Program


Geometric Aspects of the Langlands Program March 18, 2002 - March 22, 2002
Registration Deadline: March 22, 2002 over 22 years ago
To apply for Funding you must register by: December 18, 2001 over 22 years ago
Parent Program:
Organizers E. Frenkel, V. Ginzburg, G. Laumon and K. Vilonen

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The Langlands Program has emerged in the late 60's 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 recent years it was realized that the Langlands conjectures (in the function field case) may be formulated geometrically, thereby allowing one to state them over an arbitrary field (e.g., the field of complex numbers). This approach has led to Drinfeld's proof of the Langlands conjecture for GL(2) in the function field case. More recently, A. Beilinson and V. Drinfeld have proved a variant of the geometric Langlands correspondence over complex field. It relates Hecke eigensheaves on the moduli stack of G-bundles over a complex curve X and local systems for the Langlands dual group of G. They construct this correspondence via quantization of an integrable system on the cotangent bundle to the moduli space of G-bundles defined by Hitchin. Their work uses in an essential way representation theory of affine Kac-Moody algebras. On the other hand, L. Lafforgue has proved the Langlands conjecture for the case of the field of functions on a curve over a finite field. Geometry of bundles on curves with additional structures (shtukas) also plays an important role in his proof. In this workshop, we would like to bring together people working in different parts of this diverse area to enable them to learn from each other and to find points of contact between different directions. We are planning to concentrate in particular on the following topics: 1. Works of Beilinson and Drinfeld on the geometric Langlands correspondence. 2. Lafforgue's proof of the global Langlands conjecture for GL(n) in the function field case. 3. Local geometric problems, such as local models for Shimura varieties, fundamental lemma, and geometric realizations of Hecke algebras. Confirmed participants include: A. Beilinson, R. Bezrukavnikov, V. Drinfeld, G. Faltings, D. Gaitsgory, T. Haines, M. Harris, M. Kapranov, L. Lafforgue, S. Lysenko, R. MacPherson, I. Mirkovic, M. Rapoport. Group photo of participants
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Mar 18, 2002
08:00 AM - 05:00 PM
  Geometric Langlands for GL(n) and a Vanishing Conjecture
Dennis Gaitsgory (Harvard University)
09:15 AM - 09:45 AM
  Morning Tea
09:45 AM - 10:00 AM
  Welcoming Remarks
Loa Nowina-Sapinski
10:00 AM - 11:00 AM
  On Langlands correspondence in the de Rham setting, part I
Alexander Beilinson (University of Chicago)
11:00 AM - 11:30 AM
11:30 AM - 12:30 PM
  Perverse sheaves on loop Grassmannians
Ivan Mirkovic (University of Massachusetts, Amherst)
12:30 PM - 02:00 PM
02:00 PM - 03:00 PM
  Central sheaves on he affine flag variety: A prerequisite for Bezrukavnikov's work
Dennis Gaitsgory (Harvard University)
03:00 PM - 03:30 PM
  Afternoon Tea
04:10 PM - 05:10 PM
  Arthur-Selberg trace formula, Drinfeld shtukas and Langlands' correspondence
Laurent Lafforgue
Mar 19, 2002
10:00 AM - 11:00 AM
  Introduction to Shimura varieties
Gerd Faltings (Max-Planck-Institut für Mathematik)
11:30 AM - 12:30 PM
  Local models of Shimura varieties in the ramified case
Michael Rapoport (Universität Bonn)
02:00 PM - 03:00 PM
  Combinatorial patterns in the weight filtration on the nearby cycles for some Shimura varieties with bad reduction
Thomas Haines (University of Maryland)
03:30 PM - 04:30 PM
  Geometric realization of local Langlands correspondences
Michael Harris (Columbia University)
Mar 20, 2002
10:00 AM - 11:00 AM
  Pavings of polyhedra, glueing of Schubert cells and compactification of configuration spaces, part I
Laurent Lafforgue
11:30 AM - 12:30 PM
  Line-bundles on the moduli-space of G-torsors
Gerd Faltings (Max-Planck-Institut für Mathematik)
02:00 PM - 03:00 PM
  Sheaves on affine flags, and modular representations of the Langlands dual Lie algebra
Roman Bezrukavnikov (Massachusetts Institute of Technology)
03:30 PM - 04:30 PM
  p-Adic automorphic representations
Matthew Emerton (University of Chicago)
Mar 21, 2002
10:00 AM - 11:00 AM
  On Langlands correspondence in the de Rham setting, part Ii
Alexander Beilinson (University of Chicago)
11:30 AM - 12:30 PM
  Pavings of polyhedra, glueing of Schubert cells and compactification of configuration spaces, part II
Laurent Lafforgue
02:00 PM - 03:00 PM
  Uhlenbeck spaces for A^2 and affine Lie algebra $$\hat{sl}_n$$
Michael Finkelberg
03:30 PM - 04:30 PM
  An introduction to the Drinfeld-Langlands program
Gerard Laumon (Université de Paris XI)
Mar 22, 2002
10:00 AM - 11:00 AM
  Modular representations of p-adic groups and q-affine Schur algebras
Marie-France Vigneras (Université de Paris VII (Denis Diderot))
11:30 AM - 12:30 PM
  Geometric Rankin-Selberg for GL(n)
Sergey Lysenko
02:00 PM - 03:00 PM
  Formal arcs to algebraic semi-groups and automorphic L-functions
Amy Braverman
03:30 PM - 04:30 PM
  Fourier transform for quantized completely integrable systems
Dmytro Arinkin (University of Wisconsin-Madison)