Recent development in Link Homology

Organizers: Anna Beliakova (Universität Zürich), Krzysztof Putyra (Universität Zürich), Louis-Hadrien Robert (University of Luxembourg).

https://lrobert.perso.math.cnrs.fr/SRS/srs.html

Link homology theories emerged about 20 years ago with the celebrated Khovanov homology and Heegaard–Floer homology. These theories categorify respectively the Jones polynomial and the Alexander polynomial, the two most famous polynomial link invariants. These theories are likely to become an essential building block in the seek for a 3+1 quantum field theory (but many hard steps are still to be accomplished).

Since then many developments occurred and generalizations of these theories have been defined and studied. We appear to be at a crucial moment: on the one end, relationships between these different theories is more and more understood; on the other end, many new ideas have come to light in the last five years: y-ification, geometric approach via Hilbert schemes of points, Hopfological algebra, foam evaluation, etc. These new ideas raise new questions and establish connections with other mathematical fields such as (derived) algebraic geometry, homotopy theory, Schubert calculus, combinatorics, etc, while the hope to obtain a mathematical definition of a 3+1 quantum field theory is growing.

The aim of this workshop is to facilitate communication between mathematicians and theoretical physists investigating all the emerging directions coming from link homology theories. The hope is to get a better understanding of how these new ideas relate with one another and to try to clear the path to the quest of categorified 3-manifold invariants.