Victor Kac of the Massachusetts Institute of Technology will be awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement at the Joint Mathematics Meetings in January in San Antonio, Texas. He is honored for "his groundbreaking contributions to Lie Theory and its applications to Mathematics and Mathematical Physics."
Lie theory, which began with the work of the Norwegian mathematician Sophus Lie (1842-1899), provides a powerful means for extracting simple structures from highly complicated mathematical objects. It has had an impact in nearly every area of mathematics and has been a fundamental tool in several areas of physics. Finite-dimensional Lie theory "has left no part of mathematics untouched since the mid-1800s," the prize citation says. "The search for an analogous theory for infinite-dimensional Lie groups and algebras is much more recent but is no less important and fundamental. Kac has been the prime mover in creating this theory over the past 45 years."
Kac is best known for his 1967 discovery, together with Robert Moody, of what have come to be known as Kac-Moody algebras. These algebras "quickly became a basic and natural area of investigation in Representation Theory," the prize citation says. "They now are seen to form the backbone of many aspects of Combinatorics, Integrable Systems, Modular Forms, Enumerative Algebraic Geometry, and the Langlands Program. They also play an important role in Quantum Field Theory and Statistical Mechanics."
Over his long career, Kac has not only proved important results but has also led the way into new and fertile directions of research. Several generations of mathematicians have found his book Infinite-Dimensional Lie Algebras (third edition, Cambridge, 1990) to be indispensable to their education and research.
Born in the USSR in 1943, Kac received his doctorate from Moscow State University in 1968. In 1977, he came to the United States and joined the faculty of MIT. A prolific researcher, his publication list contains over 200 items written with over 65 collaborators from all five continents. In 1996 he and Moody received the Wigner Medal, and in 2013 Kac was elected to the US National Academy of Sciences.
Presented annually, the AMS Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded at the Joint Mathematics Meetings, Sunday, January 11, 2015 at 4:25 PM, at the Henry B. Gonzalez Convention Center in San Antonio, Texas.
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Founded in 1888 to further mathematical research and scholarship, today the nearly 30,000 member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.