Research subjects
My research is e.g. about this (click to enlarge):
Ok, let me give some more details.
- “Condensed research statement” (quite recent): available here.
- Research statement (quite recent): available here.
- Research statement (not up to date and quite old): available here,
here, and here.
- Higher representation theory.
- Higher category theory
(especially for ) and categorification.
- Applications in low dimensional topology (e.g. knot theory link polynomials and homologies etc.).
- Applications in the representation theory of Lie algebras, quantum groups,
diagram algebras and finite-dimensional algebras.
- 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.
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