(1)   Title: Richardson elements for seaweed Lie algebras of finite types. 

Speaker: Professor Bernt Tore Jensen (Norwegian University of Science and Technology)

Time: 3:00-4:00pm July 19, 2019 (Friday)

Place: Mathematics Building 200-9

Abstract: Let g be a reductive Lie algebra over the field of complex numbers. A Lie subalgebra q of g is called a seaweed Lie subalgebra if it is the intersection of two parabolic subalgefbras  of g such that the sum of the two subalgebras is g. In this talk we will discuss the existence of Richardson elements x for seaweed Lie subalgebras q of g in the sense that [q, x] is the whole nilpotent radical of q. We use techniques from quiver representation theory. 

(2)   Title: Towards categorification of quantum Grassmannian cluster algebras

Speaker: Professor Xiuping Su (University of Bath)

Time: 4:10-5:10pm July 19, 2019 (Friday)

Place: Mathematics Building 200-9

Abstract: Based on a cluster category CM(A), we construct compatible pairs of matrices (B(T), L(T)) from a cluster tilting object T in CM(A). We show that 

  1) when the matrix L is constructed from certain special cluster tilting objects , L computes quasi-commutation rules for quasi-commuting quantum minors.

  2) Mutation of (B(T), L(T)) is consistent with mutation of cluster tilting objects. 

  The goal of this talk is to explain how 1) and 2) lead to a quantum cluster algebra structure on a quantum Grassmannian and thus a categorification of the quantum Grassmannian cluster algebra.

contact person: Li Fang（fangli@zju.edu.cn）