Categorification and higher representation theory

Project description

Motivated by the pursuit of providing combinatorially computable 4D topological field theories that lift existing 3D theories obtained from quantum groups, categorification has grown into an active area of research combining methods from topology, representation theory, and geometry. Motivated by applications to categorification, there have been efforts to develop a theory of higher representations, called 2-representation theory, for such structures. Since 2010, Mazorchuk-Miemietz and collaborators have developed a program that categorifies the representation theory of finite-dimensional algebras. Building on this program, new directions are to be explored linking to categorification of algebraic structures involving roots of unity or derived algebraic geometry through differentially graded structures.