Seminar

I am organizing a regular seminar on Weyl/Coxter group, Springer theory, Hecke algebra and related topics.

2018-Spring Representations of Finite group and affine Hecke algebra

For 2018 Spring semester, from 28 Feb 2018 to the end of the semester.
Time: Wednesday afternoon 13:00-15:30, Week 1-17.
Venue: School of Mathematics SJTU, Room-1106.

We plan to read the following two papers.
1. Pierre Deligne and George Lusztig, Representations of Reductive Groups Over Finite Fields
2. David Kazhdan, George Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras

The tasks are divied as the following:

Speackers Deligne-Lusztig's paper
Ma Jiajun Introduction, Section 1-2
Chen Miaofen Section 3-4
TBA Section 5
TBA Section 6-7
TBA Section 8-9
TBA Section 10-11
Speackers Kazhdan-Lusztig's paper
TBA TBA

2017-Fall Minimal length elements

For 2017 Fall semester, from 11-Sep 2017 to 21-Nov 2017, the time and venue are as the following:
Time: Wednesday afternoon 13:00-15:00.
Venue: School of Mathematics SJTU, Room-1106.

Time/speaker VenueTitle/Abstract
Sep 13, 2017,
13:00-15:00
Room-1106Introduction on conjugacy classes of finite coxeter groups.
Ma Jia-JunWe will discuss the geometric interpretation of the length function of finite Coxeter groups.
Sep 20, 2017, 13:00-15:00/Ma Jia-JunRoom-1106Geometric interpretation of the length function. (cont.)
Sep 27, 2017, 14:00-15:00/Ma Jia-JunRoom-1106Proof of the main theorem on minimal length elements (for finite Coxeter group)
Oct 4, 2017Cancelled due to the national day holiday.
Oct 11, 2017Cancelled due to an event of the department.
Oct 18, 13:00-15:00/Zhang GuanglianRoom-1106Elliptic elements in Weyl groups
Oct 25, 13:00-15:00/Zhang GuanglianRoom-1106Good elements in Weyl groups
Nov 1, 13:00-15:00/Qin FanRoom-1106Introduction to affine Weyl groups.
Nov 8, 13:00-15:00/Qin FanRoom-1106minimal length element in affine groups.
Nov 15, 13:00-15:00/Qin FanRoom-1106minimal length element in affine groups (cont.)
Nov 22Cancelled
Nov 29 13:00-15:00/Chen MiaofenRoom-1106Straight conjugacy class
Dec 6 13:00-15:00/Chen MiaofenRoom-1106Straight conjugacy class and its relation to other topics.
Dec 13: 13:00-15:00/ Ma Jia-JunRoom-1106Classification of nice elements.
Dec 20 10:00-12:00/
Ma Jia-Jun
Room-1106Cocenter of an affine Hecke algebra.

2017-Spring Springer theory

For 2017 Spring semester, from 21-Mar 2017 to 27-June 2017, the time and venue are as the following:
Time: Tuesday noon 12:00-13:30. (the time slot is updated) 
Venue: School of Mathematics SJTU, Room-1106.

TimeVenueTitle/Abstract
Mar 21, 2017,
18:30-20:00
Room-1106Introduction to Springer theory
This is the first talk of my proposed seminar on Weyl group, Springer theory, Hecke algebra and related topics. As an orientation, I will first explain the content of Springer correspondence. Then I will briefly review the basic idea of the constructions of the Springer correspondence. In the end, I will discuss some relationships of the Springer theory with other fields, such as combinatorics and representation theory of reductive groups. If time permits, I will also discuss the generalized Springer correspondence.
Mar 28, 2017Canceled
April 4, 2017Canceled due to Qingming Festival
April 11, 2017,
12:00-13:30
Room-1106A proof of Springer correspondence by Chriss-Ginzburg, (I)
I will present a proof of the Springer correspondence following Chriss-Ginzburg's book "Representation Theory and Complex Geometry" in the next two or three talks. In this talk, I plan to discuss the geometry of the flag variety and the Steinberg variety.
April 18, 2017,
12:00-13:30
Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
April 25, 2017,
12:00-13:30
Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
May 2 , 2017,
12:00-13:30
Canceled
May 9 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 16 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 23 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book.
May 30 , 2017,
12:00-13:30
Canceled due to Duanwu Festival(Dragon Boat Festival)
Jun 6 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book.
Jun 13 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book.
Jun 20 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book. Finished Chapter 3