## Victor Kac

### Massachusetts Institute of Technology

Election Year: 2013 Primary Section: 11, Mathematics Secondary Section: 13, Physics Membership Type: Member |

### Biosketch

Victor Kac is a Professor of Mathematics at the Massachusetts Institute of Technology. He works in several areas of algebra and mathematical physics related to symmetries. He is known particularly for the theory of Kac-Moody algebras and the theory of Lie superalgebras, and for developing an algebraic theory of integrable systems. Kac was born in Buguruslan, Russia in 1943 and grew up in Kishinev, Moldova. He graduated from the Mechanics and Mathematics Department of Moscow State University in 1965 and three years later was awarded a Candidate of Mathematical Sciences degree. Between 1968 and 1976, he taught at the Moscow Institute of Electronic Machine Building. In 1977, after immigrating to the United States, he joined the faculty of the Department of Mathematics at M.I.T. and in 1982 became a U.S. citizen. He is married and has two daughters. Kac is an honorary member of the Moscow Mathematical Society, and a fellow at the American Academy of Arts and Sciences and the National Academy of Sciences. Kac's awards include the Medal of the College de France and the Wigner Medal. He was a plenary speaker at the Centennial of the American Mathematical Society and at the International Congress of Mathematicians in Beijing.

### Research Interests

The research of Victor Kac primarily concerns algebra and mathematical physics. Here are some of his best known results and discoveries: 1. Classification of infinite-dimensional Lie algebras of polynomial growth, which included affine Kac-Moody algebras. 2. Kac-Weisfeiler representation theory of Lie p-algebras. 3. Weyl-Kac character formula. 4. Theory of finite-dimensional Lie superalgebras. 5. Linear algebraic groups with nice properties of orbits and invariants. 6. Typical representations of simple Lie superalgebras. 7. Kac determinant formula for representations of the Virasoro algebra. 8. Frenkel-Kac vertex operator construction. 9. Kac polynomials for indecomposable representations of quivers. 10. Kac-Peterson cocycle. 11. Kac-Peterson theorem on modular invariance of affine characters. 12. Kac-Peterson theory of Kac-Moody groups. 13. Dadok-Kac theory of polar representations. 14. Kac-Wakimoto spectrum of modular invariant representations. 15. Kac-Wakimoro hierarchies of PDE. 16. Deconcini-Kac-Procesi theory of quantum groups at roots of 1. 17. Kac-Wakimoto character formula for affine Lie superalgebras and number theory. 18. Classification of infinite-dimensional simple linearly compact Lie superalgebras. 19. D'Andrea-Fattori-Kac classification of finite simple Lie conforma (super)algebras. 21. Bakalov-D'Andrea-Kac theory of Lie pseudoalgebras. 21. Kac-Rudakov representation theory of E(3,6). 22. Cantarini-Kac structure theory of linearly compact Lie superalgebras. 23. De Sole-Kac algebraic theory of integrable systems. 24. Kac-Wakimoto characters for affine Lie superalgebras and mock theta functions.