# Mathematics Colloquium Winter 2018

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**