Webinar on algebraic combinatorics and Lie theory
（与南开大学数学院共同承办）
时间：2022年3月19日，20日
地点：Zoom会议：694 0835 1616
日程：
19日，09：00-09：45
题目：Integral points and frieze points in double Bruhat cells
报告人：Antoine de Saint Germain （香港大学）
摘要：In this talk, I will introduce the notion of an integral point in a simply connected Lie group G, and discuss some of its properties. I will then relate these points to Luzstig’s notion of total positivity on G. As a special case, I will discuss frieze points in G - a geometric analogue of the classical notion of a frieze introduced by Coxeter in the 1970s.
19日，10：15-11：00
题目：Geometric multiplicities
报告人：李彦鹏（四川大学）
摘要：In this talk, I will introduce geometric multiplicities, which are positive varieties with potential fibered over the Cartan subgroup $H$ of a reductive group $G$. They form a (unitless) coboundary category $Mult_G$ and we construct a monoidal functor from $Mult_G$ to the representation category of the Langlands dual group $G^\vee$ of $G$. In particular, by using this functor, we recover the formulas for tensor product multiplicities and for reduction multiplicities to Levi subgroups obtained by Berenstein-Zelevinsky in 2001 and generalize them in several directions. This is joint work with Arkady Berenstein.
20日，09：00-09：45
题目：Newton Polytopes in Algebraic Combinatorics
报告人：郭龙 （南开大学）
摘要：In this talk, we shall investigate the Newton polytopes of several important
families of polynomials in algebraic combinatorics, including for example Schur polynomials, Schubert polynomials, Grothendieck polynomials, key polynomials.
20日，10：15-11：00
题目：Polyubles and Poisson homogenous spaces
报告人：于世卓（南开大学）
摘要：Polyubles are constructions of "n-th power" of Manin triples, which can be used to construct a class of Poisson structures on homogenous spaces. In this talk, we first introduce a class of isomorphisms between them . Then, we apply these isomorphisms to a class of Poisson homogenous spaces, including concrete examples related to multi-flag varieties.