Mathematics Colloquium Winter 2018

Tuesdays - 4:00 p.m.
McHenry Library Room 4130
Refreshments served at 3:30 in the Tea Room (4161)
For further information please contact Professor Torsten Ehrhardt or call the Mathematics Department at 459-2969

Tuesday, January 9, 2018

No Colloquium


Tuesday, January 16, 2018

No Colloquium


Tuesday, January 23, 2018

ZongZhu Lin, Kansas State University

Comparing of Highest Weight Representations of Various Forms of Quantum Groups

In 1979, Kazhdan and Lusztig conjectured a formula computing the characters of irreducible highest weight representations of a finite dimensional semisimple complex Lie algebra in terms of combinatorial data of the corresponding Weyl group. This conjecture and many other analogs, in fact, imply that many different categories, being from geometry, or representations of Lie algebras, algebraic groups, quantum groups are equivalent. The approach in proving the conjectures is to formulate certain categories that can link different representation theories and to establish the categorical equivalences. In the talk, I will first survey some of the main approaches, in particular, of Lusztig’s series of conjectures comparing representations of quantum groups, affine Lie algebras, Lie super algebras, and algebraic groups. Then I will introduce a new frame work to compare certain classes of weighted representations of Lie algebras and quantum groups as well as their variations and prove that, despite the algebras are different, they share a common weighted representation theory. This new framework follows from Lusztig’s constructions of modified quantum groups. This work is joint with Zhaobing Fan and Yigiang Li.


Tuesday, January 30, 2018

Pham Tiep, Rutger's University

Representations of Finite Groups and Applications

In the first part of the talk we will survey some recent results on representations of finite groups. In the second part we will discuss applications of these results to various problems in group theory, number theory, and algebraic geometry. 


Tuesday, February 6, 2018

TBA


Tuesday, February 13, 2018

Gunter Malle, University of Kaiserslautern


Tuesday, February 20, 2018

TBA


Tuesday, February 27, 2018

TBA


Tuesday, March 6, 2018

TBA


Tuesday, March 13, 2018

TBA