Quantum topology: the case of odd Khovanov homology

Quantum topology studies homological invariants of knots stemming from representation theory. These invariants are typically combinatorially defined and hence easily computable; the downside being that the topology they capture is hard to grasp. An important question is to relate them to another family of homological invariants, stemming instead from gauge theory and symplectic geometry, which are typically hard to compute but whose topological meaning is clearer. One quantum invariant in particular, known as odd Khovanov homology, is believed to be a cornerstone to this question; yet, it remains badly understood.

This short talk with give an overview on quantum topology, with odd Khovanov homology as a study case.