Abstracts for Quantum topology seminar

Classical quantum topology studies polynomial invariants of links arising from the representation of quantum groups — in particular, the sln-Jones polynomial, associated to quantum sln. Around 2000, it was realized that some of these polynomial invariants generalize (“categorify”) to homological invariants — in particular, Khovanov–Rozansky homology categorifying the sln-Jones polynomial. This homology can be defined in various ways, including using matrix factorisation, category O, the algebraic geometry of flag varieties, or defect TQFTs. String diagrams for higher categories, i.e.