Research subjects

My research is e.g. about this (click to enlarge):

Ok, let me give some more details.
  1. Research statement (quite recent): available here.
  2. Research statements (not up to date and quite old): available here, here, here, and here.
  3. Higher representation theory.
  4. Higher category theory (especially for ) and categorification.
  5. Applications in low dimensional topology (e.g. knot theory link polynomials and homologies etc.).
  6. Applications in the representation theory of Lie algebras, quantum groups, diagram algebras and finite-dimensional algebras.
  7. Some talks of mine for a more general (mathematical) audience: Talk1, Talk2, Talk3, Talk4, Talk5, Talk6

In short: My main research interest is $2$-categorical representation theory (of e.g. categorified Coxeter groups), categorification (of e.g. quantum groups) and its applications in representation theory, low dimensional topology and algebraic geometry. In particular, I am interested in algebraic, combinatorial and diagrammatic aspects of categorification. I am also interested in related topics as for example representation theoretical questions about Hecke/Brauer algebras or Lie groups and modular representation theory.