## String-Math Seminar: Searching for Lie groups of the XXI century

Seminar | May 6 | 2-3 p.m. | 402 LeConte Hall

Andrei Okounkov, Columbia University

Department of Mathematics

It has been understood for some time now that many highlights of Lie theory, such as the representation-theoretic theory of special functions, or the Kazhdan–Lusztig theory, have a natural extension to a much broader setting, the boundaries of which are yet to be explored. In this extension, the focus is shifting from a group $G$ to various classes of algebraic varieties that possess the key features of $T^*G/B$. While there are some proposal about what should replace a Lie algebra, root systems, etc., it is less clear what should be the group, or multiplicative analog of these structures. Reflecting the nature of the field, the talk will combine a review of established partial results with unsubstantiated speculations.

artamonov@berkeley.edu