Speaker: Dmitry A. Timashev, professor, Lomonosov Moscow State University

Date: May 8, 2024; May 13, 2024; May 15, 2024

Time: 14:00-16:00

Location: B1044, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Spherical varieties constitute a remarkable class of rational algebraic varieties including many classical examples, such as projective spaces, quadrics, Grassmannians, flag varieties, determinantal varieties, etc., and also toric varieties, wonderful completions of symmetric spaces, and other important cases. Sphericality is not justa geometricproperty of a variety, but rather a property of an algebraic group action. Still it has important implications both in geometry of a variety and in related representation-theoretic issues. In fact, spherical varieties lie at the crossroads of algebraic geometry, theory of algebraic groups, enumerative geometry, harmonic analysis, and representation theory.

This mini-course is aimed at introducing basic notions and facts about spherical varieties and some applications of the theory. We start with homogeneous spherical varieties, also known as spherical homogeneous spaces, and discuss their geometric and representation-theoretic properties. General spherical varieties can be viewed as equivariant (partial) compactifications of spherical homogeneous spaces. Such compactifications can be classified and studied in terms of convex geometric and combinatorial data in a way similar to the theory of toric varieties. We shall develop this approach and discuss some applications including theory of divisors and line bundles on spherical varieties, solving enumerative problems on spherical homogeneous spaces, and problems in representation theory such as tensor product decompositions.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/190521.htm