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Workshop

Conformal Field Theory and Supersymmetry April 15, 2002 - April 26, 2002
Registration Deadline: April 26, 2002 over 16 years ago
To apply for Funding you must register by: January 15, 2002 almost 17 years ago
Parent Program:
Organizers G. Felder, D. Freed, E. Frenkel, V. Kac, T. Miwa, I. Penkov, V. Serganova, I. Singer and G. Zuckerman
Speaker(s)

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Description
Week 1: "Infinite-dimensional Algebras, Conformal Field Theory and Integrable Systems" Some of the most spectacular applications of representation theory of infinite-dimensional algebras are related to recent developments in mathematical physics. Conformal quantum field theory (CFT) in two dimensions and string theory have a multitude of deep connections to the representation theory of infinite algebras. In a sense the two subjects have been joined at the hip since their inception in the late 1960's. The early physics papers on string theory introduced representations of the Virasoro Lie algebra and quantum fields known as vertex operators. By the early 1980's it was realized that the Virasoro algebra is a universal symmetry algebra of a 2D CFT, and that affine Kac-Moody algebras (central extensions of loop algebras) are symmetry algebras of CFTs of a more special type (Wess-Zumino-Witten models). Eventually, Borcherds succeeded in formalizing the general notion of a symmetry algebra of a CFT in the concept of vertex algebra. More recently, Beilinson and Drinfeld have introduced a geometric version of vertex algebras which they call chiral algebras. Chiral algebras give rise to some novel concepts and techniques in algebraic geometry, in particular, in the geometric Langlands correspondence. Physicists have recently begun to study perturbations of conformal field theories in the hopes of using the rich structure of CFT for understanding more general integrable quantum field theories. The study of conformal field theory in dimensions greater than two is also under way, and surprising connections have been found between these theories and string theory (AdS/CFT correspondence). Infinite-dimensional algebras have also been used in the recent years in the theory of exactly solved models. It turned out that quantum deformations of the enveloping algebras of the affine Kac-Moody algebras, the Virasoro algebra, and the W-algebras may be realized as dynamical symmetry algebras of various lattice models, and hence their representation theory has important applications. Infinite-dimensional Lie algebras also play a central role in the study of integrable systems, such as those associated to the KdV equation and other soliton hierarchies. These integrable systems appear in the study of the Gromov-Witten invariants of algebraic manifolds. The Virasoro conjecture, in particular, indicates the relevance of infinite-dimensional algebras in this area. In this workshop we will discuss the areas mentioned above and interactions between them. Week 2: "Supersymmetry in Mathematics and Physics" Supersymmetry is now considered as one of the most fundamental concepts in physics. Lie superalgebras in particular have increasingly been playing central role in recent studies of quantum field theory and string theory. There has also been an important development in mathematics, like structure and representation theory of Lie superalgebras, "supersymmetric" proofs of the index theorems, the theory of superconnections, etc. In this workshop, we hope to discuss the recent advances in "superphysics" and "supermathematics."          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
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, 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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A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

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Schedule, Notes/Handouts & Videos
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Apr 15, 2002
Monday
08:00 AM - 05:00 PM
  TBA
Anton Kapustin
09:15 AM - 09:45 AM
  Morning Tea
09:45 AM - 10:00 AM
  Welcome & Introduction
Loa Nowina-Sapinski
10:00 AM - 11:00 AM
  Frobenius manifolds and integrable systems
Boris Dubrovin (Scuola Internazionale Superiore di Studi Avanzati (SISSA))
11:30 AM - 12:30 PM
  Sl_2 loop algebra symmetery in the six vertex model at roots of unity
Barry McCoy
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Strings in AdS_3 and the SL(2,R) WZW model
Hirosi Ooguri
03:00 PM - 03:30 PM
  Afternoon Tea
04:10 PM - 05:10 PM
  Some mathematical problems in Conformal Field Theory
Jean-Bernard Zuber
Apr 16, 2002
Tuesday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Exploring a moduli space: CFT on K3
Werner Nahm
11:30 AM - 12:30 PM
  Quantum Liouville theory versus quantum Teichmueller space
Joerg Teschner (Universität Hamburg)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Conformal Field Theory associated to regular chiral vartex operator algebras
Akihiro Tsuchiya
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Gauss-Selberg sums
Ivan Cherednik (University of North Carolina)
04:30 PM - 05:30 PM
  Reception
Apr 17, 2002
Wednesday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Tensor categories and orbifold vertex algebras
Alexander Kirillov
11:30 AM - 12:30 PM
  Affine Kac-Moody algebras and geometric Langlands correspondence
Edward Frenkel (University of California, Berkeley)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Representation theory beyond affine Lie algebras: A perspective
Igor Frenkel
03:15 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Semisimplicity of orbifold vertex algebras
Alexander Voronov
Apr 18, 2002
Thursday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Quantization of affine Jacobian and duality
Fedor Smirnov
11:30 AM - 12:30 PM
  Conformal Field Theory as a completely integrable quantum system
Vladimir Bazhanov
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Formal group laws for infinite-dimensional Lie algebras
Richard Borcherds (University of California, Berkeley)
03:00 PM - 03:15 PM
  Afternoon Tea
03:15 PM - 04:15 PM
  Vertex algebras and mirror symmetry
Anton Kapustin
04:30 PM - 05:30 PM
  Generalized Kirillov-Reshetkhin modules over quantum affine algebras
Ian Grojnowski
Apr 19, 2002
Friday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Ideals in the Weyl algebra
George Wilson
11:30 AM - 12:30 PM
  Matrix integrals, random words and walks
Pierre van Moerbeke
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Operator algebraic analysis of solvable lattice models
Antony Wassermann
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Local conformal field theory
Feng Xu
Apr 22, 2002
Monday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Group-theoretic and low-dimensional origins of supersymmetry
Sylvester Gates
11:30 AM - 12:30 PM
  Introduction to supersymmetry
Dan Freed (University of Texas, Austin)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Gauge theories on noncommutative spaces
Bruno Zumino
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Representations of linearly compact Lie superalgebras and the Standard Model
Victor Kac
Apr 23, 2002
Tuesday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Superconnections in geometry, commutative and noncommutative
John Lott (University of California, Berkeley)
11:30 AM - 12:30 PM
  Variations of Hodge structure associated to Calabi-Yau three folds with h^3=4
John Morgan (Columbia University)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Representations and characters for Lie superalgebras
Vera Serganova (University of California, Berkeley)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  The centre of P-type Lie superalgebra
Maria Gorelik (Weizmann Institute of Science)
Apr 24, 2002
Wednesday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  D-branes, supersymmetry, and mirror symmetry
Kentaro Hori
11:30 AM - 12:30 PM
  Del Pezzo surfaces in string theory
Amer Iqbal
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Chiral De Rham Complex
Arkady Vaintrob
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  N=2 Supersymmetry of Super KP Equations
Jeff Rabin
Apr 25, 2002
Thursday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  Convexity theorems and the order relation on nilpotents based on orbit closure
Bertram Kostant
11:30 AM - 12:30 PM
  Maximally supersymmetric gauge theories
Albert Schwarz
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Superstring scattering amplitudes and modular forms
Duong Phong
03:00 PM - 03:30 PM
  Afternoon Tea
04:10 PM - 05:10 PM
  (Math Dept. Colloquium, Evans Hall Rm. 60) From numbers to q-numbers to elliptic numbers: The elliptic gamma function
Giovanni Felder (ETH Zürich)
Apr 26, 2002
Friday
09:30 AM - 10:00 AM
  Morning Tea
10:00 AM - 11:00 AM
  From unique factorization of graphs to gauge symmetries
Dirk Kreimer
11:30 AM - 12:30 PM
  On representations of contact superconformal algebras
Elena Poletaeva
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  A generalization of Harish-Chandra's discrete series to Lie superalgebras
Gregg Zuckerman
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Hodge theory and supersymmetry on Kahler, hyperkahler, and hyperkahler torsion manifolds
Misha Verbitsky