Columbia University G6306
Introduction to categorification

Basic information

Semester: Spring 2020
Call number: 13901
Room/Time: TuTh 4:10pm--5:25pm, 507 Math
Instructor: Mikhail Khovanov
Office: 620 Math
Office Hours: Walk-in or by appointment


This course will deal with the lifting of quantum link invariants to homology theories of links and their extensions to tangle and cobordism invariants. It will cover construction of link homology theories via foams and matrix factorizations, categorification of quantum groups and their representations, and related topics in representation theory and low-dimensional topology.

Notes by Qi You from an earlier course:

1. Introduction      
2. Topological Quantum Field Theories
3. Categorification of the Jones polynomial
4. Grothendieck groups
5. Extending link homology to tangles
6. Milnors conjecture
7. Biadjoint functors
8. sl(3) link homology
9. Morita theory
10. Hochschild homology and applications to link homology I
11. Hochschild homology and applications to link homology II
12. Categorification of the Heisenberg algebra
13. Hopf algebras