Geometric Representation Seminar
Student No.:40
Time:Fri 13:30-15:00
Instructor:Shan Peng  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-3-9
Ending Date:2018-6-15




Speaker: 余世霖 Yu Shilin [Texas A&M University]

Title: Quantization and representation theory

Abstract: In this talk, I will talk about a geometric way to construct representations of noncompact semisimple Lie groups. Kirillov's coadjoint orbit method suggests that (unitary) irreducible representations can be constructed as geometric quantization of coadjoint orbits of the group. Except for a lot of evidence, the quantization scheme meets strong resistance in the case of noncompact semisimple groups. I will give a new perspective on the problem using deformation quantization of symplectic varieties and their Lagrangian subvarieties. This is joint work in progress with Conan Leung.





Speaker: 董志杰 Dong Zhijie [University of Massachusetts Amherst]

Title: A relation between Mirković-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE

Abstract: The irreducible components of the variety of all modules over the preprojective algebra and MV cycles both index bases of the universal enveloping algebra of the positive part of a semisimple Lie algebra canonically. To relate these two objects Baumann and Kamnitzer associate a cycle in the affine Grassmannian for a given module. It is conjectured that the ring of functions of the T-fixed point subscheme of the associated cycle is isomorphic to the cohomology ring of the quiver Grassmannian of the module. I will talk about a partial proof of this conjecture and discuss some relation to Hikita Conjecture and Coulomb branch.