iTHEMS Math Seminar by Mikhail Khovanov on May 28, 2026

On May 28, 2026, iTHEMS hosted a special iTHEMS Math Seminar, “Introduction to Categorification and Link Homology,” delivered by Professor Mikhail Khovanov of Johns Hopkins University. The event was held in a hybrid format at Okochi Hall and via Zoom, with more than 80 participants attending in person and over 70 joining online.

Professor Khovanov is a leading mathematician whose work has had a major influence on knot theory, low-dimensional topology, representation theory, and mathematical physics. He is especially well known for introducing the categorification of the Jones polynomial, now called "Khovanov homology".

In the talk, Professor Khovanov introduced the idea of “categorification” by starting from the classical relationship between the Euler characteristic and homology groups in topology. He then discussed the Jones polynomial, a knot invariant introduced by mathematician V. F. Jones in the 1980s, with particular emphasis on its representation-theoretic interpretation. He explained how this invariant can be lifted to a homology theory, guiding the audience toward the construction of Khovanov homology. He concluded the talk by mentioning future directions of the theory, including its connections to algebraic geometry and geometric representation theory.

Reported by Taketo Sano