Geometric Representation Seminar
Student No.:40
Time:Wednesday 10:00-11:30, 2018.1.10
Instructor:Shan Peng  
Place:Conference Room 1, Jin Chun Yuan West Building
Starting Date:2017-12-20
Ending Date:2018-2-3




Speaker: Thomas Nevins [UIUC]


Time: Friday 10:00-11:30, 2018.2.2

Place: Conference Room 1, Jin Chun Yuan West Building

Title: Cohomology of quiver varieties and other moduli spaces
Abstract: Nakajima's quiver varieties form an important class of algebraic symplectic varieties.  A quiver variety comes naturally equipped with certain "tautological vector bundles"; I will explain joint work with McGerty that shows that the cohomology ring of the quiver variety is generated by the Chern classes of the tautological bundles.  Analogous results (work in preparation with McGerty) also hold for the Crawley-Boevey-Shaw "multiplicative quiver varieties," in particular for twisted character varieties; and the cohomology results in both cases generalize to other cohomology theories, derived categories, etc.  I hope to explain the main ideas behind the proofs of such theorems and how they form part of a general pattern in noncommutative geometry.





Speaker: 徐斌Xu Bin [YMSC]


Time: Wednesday 10:00-11:30, 2018.1.10

Place: Conference Room 1, Jin Chun Yuan West Building

Title: Arthur packets and microlocal geometry
Abstract: The irreducible admissible representations of Arthur class are the local components of automorphic representations. They are conjectured to be parametrized by the Arthur parameters, which give rise to a subset of the usual Langlands parameters. The set of irreducible representations associated with a single Arthur parameter is called an Arthur packet. On the other hand, Adam-Barbasch-Vogan (1992) (in real case) and Vogan (1993) (in the p-adic case) defined a set of irreducible admissible representations for each Langlands parameter through the microlocal geometry on certain parametrizing space of Langlands parameters, which will be called ABV-packet. Moreover, they suggested for those Langlands parameters coming from Arthur parameters, the ABV-packets are exactly the Arthur packets. It is a joint project with Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui and James Mracek that we would like to prove this statement for p-adic reductive groups in certain cases. In this talk, I will mainly describe our project and discuss some of its consequences on both representation theory and geometry.  





Speaker: 裴度Pei Du [Caltech & QGM, Aarhus University]


Time: Friday 10:00-11:30, 2017.12.22

Place: Conference Room 1, Jin Chun Yuan West Building

Title: An E_6 Surprise
Abstract: In this lecture, we will study SU(3) fusion coefficients and their deformations. We will find that they enjoy enhanced symmetries predicted by string theory and quantum field theory.