MSRI Introductory Workshop:
Homology Theories of Knots and Links

Aaron Lauda

Here are two introductory lectures on categorified quantum groups based on my joint work with Mikhail Khovanov.

1. "Diagrammatic categorification of quantum groups I": categorifying sl(2), slides, printable pdf
2. "Diagrammatic categorification of quantum groups II", slides, printable pdf

1. Homework on categorified sl(2). (Solutions)

These lectures are based on the following papers:

1. A categorification of quantum sl(2), A.L, arXiv:0803.3652
2. A diagrammatic approach to categorification of quantum groups I, Mikhail Khovanov and A.L., arXiv:0803.4121

Related papers:

1. Derived equivalences for symmetric groups and sl2-categorification, J.Chuang and R. Rouquier, arXiv:math/0407205
2. 2-Kac-Moody algebras , R. Rouquier, arXiv:0812.5023
3. Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras , J. Brundan, A. Kleshchev, arXiv:0808.2032
4. Homogeneous Representations of Khovanov-Lauda Algebras, A. Kleshchev, A Ram, arXiv:0809.0557
5. Knot invariants and higher representation theory, B. Webster, arxiv:1001.2020
6. Categorified quantum sl(2) and equivariant cohomology of iterated flag variet\ ies, A.L, arXiv:0803.3848
7. A diagrammatic approach to categorification of quantum groups II, Mikhail\ Khovanov and A.L., arXiv:0804.2080
8. A diagrammatic approach to categorification of quantum groups III, Mikhai\ l Khovanov and A.L., arXiv:0807.3250