This workshop is devoted to the large N expansion in quantum Yang Mills theory, particularly in the explicitly solvable 2D setting. During the 90's a series of articles by such physicists as D. J. Gross, W. Taylor, G. Matytsin, M. Douglas, V. Kazakov, and G. Moore produced a series of conjectured expansions for objects of 2D Yang-Mills with gauge group U(N), such as the partition function of a closed surface of genus g, the partition function of a cylinder, the expected value of the Wilson loop functional, as well as certain characters É‘R(U). These quantities are related to traces and other invariants of heat kernels, as well as to volumes and traces over moduli spaces of flat connections. The asymptotics of the partition functions are governed by statistics of branched covers of surfaces. Among the topics of the conference:
- The Matytsin asymptotics for the characters É‘R(U), recently proven by A. Guionnet and O. Zeitouni
- The Kazakov-Douglas phase transition in g = 0, recently proven by A. Boutet de Monvel and M. Shcherbina
- Zelditch's limit formula for the partition function on the cylinder
- Statistics of branched covers (integrals over Hurwitz spaces)
- Volumes and trace integrals over moduli spaces of flat bundles
- The large N limit of objects of SN
- Relations between large N theory of YM2 and random matrix models
- Relations with free probability
- The new, very fast developing work of Dijkgraaf-Vafa.
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Physics:
M. Douglas (Rutgers), J. Harnad (CRM & Concordia), V. Kazakov (École Normale), D. Korotkin (Concordia), I. Kostov (Saclay), M. Staudacher (Max Planck).
Mathématics:
P. Bleher (IUPUI), C. Frohman (SUNY), W. Goldman (Maryland), A. Guionnet (UMPA-Lyon), F. Labourie (Paris-Sud), A. Okounkov (Berkeley), N. Reshetikhin (UC Berkeley), M. Shcherbina (Kharkov), R. Wentworth (Johns Hopkins), C. Woodward (Rutgers), O. Zeitouni (Technion), S. Zelditch (Johns Hopkins)
(*) to be confirmed
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This workshop will take place at the [Far Hills Inn], in the ski-resort town of Val Morin, about 150 km north of Montreal. This charming inn will provide an intimate setting for the worshop. The inn also offers many opportunities for various activities. What's more, the inn's kitchens provide exquisite food! The lectures will begin on January 5, 2004 (Monday), and will end in the morning on January 9, 2004 (Friday). Accomodation at the Far Hills Inn is $98/person/night (double occupancy) or $118/person/night (single occupancy), taxes and service included. The dollar amounts are all in Canadian currency. This includes the room and three meals per day. We will arrange for a shuttle to travel from Montreal to the Far Hills Inn on Sunday, January 4, 2004, and back again on Friday, January 9, 2004. Please note that attendance at the workshop will be limited to approximately 50 participants, because of the limited number of rooms available at the Far Hills Inn. We therefore encourage people to register early!
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