University of Sydney Algebra Seminar

Anatol Kirillov (Research Institute for Mathematical Sciences, Kyoto University)

Friday 30th April, 12.05-12.55pm, Carslaw 175

A "small" grand unification

There are theories of classical, basic and elliptic hypergeometric series; rational, trigonometric and elliptic Dunkl operators; classical, (small) quantum and elliptic cohomology and K-theory of flag varieties (classical and quantum Schubert and Grothendieck Calculi). I will try to explain that all the theories mentioned above correspond to different representations of a certain "universal" noncommutative quadratic algebra. The main goal of my talk will be to draw attention to that quadratic algebra and to describe some of its algebraic and combinatorial properties. The main part of my talk will be elementary and should be accessible to a wide audience.