Curriculum vitae (English)
Complex algebraic and differential geometry: canonical metrics in Kaehler geometry and algebro-geometric stability. You may have a look at Richard Thomas' 2005 notes for a nice introduction to the topic. Here is a more up to date discussion of some aspects of the theory .
Donaldson-Thomas invariants and their wall-crossing: connections to integrable systems and mathematical physics; connections to representation theory of quivers and plane tropical curves. See Richard Thomas' original paper for an introduction. Some recent developements are reviewed here and here.