About:

ICMS Mathematics Colloquium: Exceptional de Rham Complexes

Prof Victor Kac (he/him), MIT

Join us in-person for this Mathematics Colloquium at ICMS. 

This event will be in G.03 on the ground floor of the Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT.

There will be a drinks and snacks reception afterwards. 

Professer Kac is one of the most distinguished and successful researchers in mathematics and physics and this will be a very high-level talk aimed at mathematicians.

About the talk:

By a celebrated theorem of E. Cartan, a simple infinite-dimensional Lie algebra of vector fields on a finite-dimensional manifold is isomorphic to one of the following Lie algebras: all vector fields, divergence zero vector fields on a manifold with a volume form, Hamiltonian vector fields on a symplectic manifold, and contact vector fields on a contact manifold. For each of these there is the associated de Rham complex, consisting of "degenerate" modules over these Lie algebras. With the advent of supersymmetry theories in physics the problem of extending Cartan's classification to supermanifolds naturally arose. In my talk I will explain the extension of Cartan's theorem to Lie superalgebras of vector fields on a finite-dimensional supermanifold. It turned out that the theory is much richer: there are, up to an isomorphism, 10 series and 5 exceptional simple infinite-dimensional Lie superalgebras of vector fields on a finite-dimensional supermanifold. I will sketch a proof of this theorem. Furthermore, it tuned out that for the exceptional Lie superalgebras the degenerate modules can be neatly arranged in an infinite number of complexes, called the exceptional de Rham complexes.

About the speaker:

Professor Victor Kac received his A.B. in 1965 and his PhD in 1968 from Moscow State University. Ernest Vinberg was his scientific advisor. Professor Kac taught at the Moscow Institute of Electronic Machine Building in 1968-1976, emigrating to the US and joining MIT mathematics faculty in 1977 (professor 1981).