Organized by: Eugene Gorsky, Sergei Gukov, Mikhail Khovanov, Andrei Negut, and Piotr Sułkowski
Categorification is one of the deepest ideas in contemporary mathematics. As the name indicates, it aims to generalize various statements to a categorical level, replacing sets by categories, functions by functors, etc. It led to important developments in various branches of mathematics, among others in knot theory (where polynomial knot invariants turned out to arise simply as dimensions of certain homological spaces, such as Khovanov homology and its generalizations), or in the algebro-geometric setting (involving objects such as coherent sheaves on Hilbert schemes of points). At the same time, categorification turns out to be related to physics, in particular to the process of quantization, and to various fundamental aspects of quantum field theory and string theory.
This workshop will focus on various aspects of categorification in mathematical physics, with particular emphasis on geometric and representation theoretic approaches to conceptualizing and computing knot invariants, and their relations with supersymmetric field theories and string theory.