Monday, April 24, 2023.

8:00 AM (Los Angeles), 11:00 AM (Toronto, New York), 5:00 PM (Zurich, Paris) 6:00 PM (Tel-Aviv)

Victor Kac


Exceptional de Rham complexes


A celebrated theorem of E. Cartan says that a simple infinite-dimensional Lie algebra of vector fields on a finite-dimensional manifold is isomorphic to one of the four series of Lie algebras: of all vector fields, of divergence zero vector fields on a manifold with a volume form, of Hamiltonian vector fields on a symplectic manifold, and of contact vector fields on a contact manifold. For each of them there is the associated de Rham complex, consisting of “degenerate” modules over these Lie algebras. In my talk I will explain an extension of this theorem to Lie superalgebras of vector fields on a finite-dimensional supermanifold. It turns out that the theory is much richer: there are, up to an isomorphism, 10 series and 5 exceptional infinite-dimensional Lie superalgebras of vector fields on a finite-dimensional supermanifold. For the latter the degenerate modules can be arranged in an infinite number of complexes, called the exceptional de Rham complexes.

A video of this lecture is available below.

About the Speaker

Professor Victor Kac earned his A.B. in 1965 and his PhD in 1968 from Moscow State University under the supervision of Professor Ernest Vinberg. After teaching at the Moscow Institute of Electronic Machine Building from 1968-1976, he immigrated to the US and joined the MIT mathematics faculty in 1977. He was appointed as a professor in 1981.
Professor Kac’s research primarily concerns representation theory and mathematical physics. He made great contributions to the development of quantum field theory, string theory, and the theory of integrable systems, particularly in the areas of Kac-Moody algebras and Lie superalgebras. Professor Kac has authored five books and over 250 articles in mathematics and physics journals.
In recognition of his influential work, Professor Kac has received many prestigious awards, including the medal of the College de France (1981), the Eugene Wigner medal (1994), and the Steele Prize for Lifetime Achievement of the AMS (2015). He has also been appointed to numerous distinguished research positions, including the Chaire Condorcet at Ecole Normale Superieure (1998), the Simons Research Visiting Professorship at MSRI (2002), and the Sarojini Damadaran Fellowship at Tata Institute for Fundamental Research (2003). Professor Kac was a plenary speaker at the AMS centennial conference in 1988 and at the ICM in 2002. He is an honorary member of the Moscow Mathematical Society (1998), a fellow of the American Academy of Arts and Sciences (2007), a member of the National Academy of Sciences (2013), and a member of the National Italian Academy, Accademia dei Lincei (2019).

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Vinberg Distinguished Lecture Series Scientific Committee

Nikolay Bogachev​

Sasha Kolpakov​

Alex Kontorovich

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