Higher Structures in Mathematical Physics
October 19th -22nd, 2010

Aaron Lauda

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

1. "Diagrammatic categorification of quantum groups I: quantum knot invariants and diagrammatic algebra" , slides, printable pdf
2. "Diagrammatic categorification of quantum groups II: categorifying quantum sl2" , slides, printable pdf
3. "Diagrammatic categorification of quantum groups III: categorifying quantum Kac Moody algebras", slides, printable pdf
4. "Diagrammatic categorification of quantum groups IV: categorifying irreducible representations, slides, printable pdf

1. Homework on diagrammatic algebra.
2. Homework on categorified sl2.

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 varieties, 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, Mikhail Khovanov and A.L., arXiv:0807.3250