CONFÉRENCE D'INTRODUCTION PAR V. GUILLEMIN ET A.A. KIRILLOV

tenue au CRM

29 octobre - 1er novembre 2001

Horaire

V. GUILLEMIN (MIT)
The convexity theorem and moment polytopes
If G is an n-torus and M a compact Hamiltonian G-manifold, the moment image of M in the dual of the Lie algebra of G is a convex polytope. This theorem, the abelian convexity theorem, was proved by Atiyah and independently by Shlomo Sternberg and myself twenty years ago in 1981. Two years later Frances Kirwan generalized this theorem to non-abelian compact groups; and subsequently there have been a host of other generalizations (among them convexity theorems involving Hamiltonian actions of loop groups). In these lectures I will try to give an overview of the history of these developments and describe some recent contributions of "moment techniques" to equivariant symplectic geometry.

A.A. KIRILLOV (Pennsylvania)
The Virasoro group and related complex geometry
1. Infinite-dimensional Lie groups and Lie algebras: main differences between them and finite-dimensional case. 2. Remarkable examples of infinite-dimensional Lie groups and Lie algebras: Vect M = Lie(Diff M), Mg = Map (M, g) = Lie (MG), Kac-Moody algebras and Kac-Petersson groups, Virasoro Lie algebra and Virasoro-Bott group. 3. Coadjoint orbits and representations of some groups listed above. The analog of the flag manifold M for the Virasoro-Bott group. 4. The quantum field approach to the study of the infinite-dimensional homogeneous Kahler manifold M (after Krichever, Zabrodin and Takhtajan).

LUNDI 29 OCTOBRE

13:30                               V. Guillemin "The convexity theorem and momen tpolytopes" I

15:00                               A.A. Kirillov "The Virasoro group and related complex geometry" I

MARDI 30 OCTOBRE

13:30                               V. Guillemin "The convexity theorem and moment polytopes" II

15:00                                A.A. Kirillov "The Virasoro group and related complex geometry" II

MERCREDI 31 OCTOBRE

13:30                               V. Guillemin "The convexity theorem and momen tpolytopes" III

15:00                               A.A. Kirillov "The Virasoro group and related complex geometry" III

JEUDI 1er NOVEMBRE

13:30                               V. Guillemin "The convexity theorem and moment polytopes" IV

15:00                                A.A. Kirillov "The Virasoro group and related complex geometry" IV