JGU Mainz

Research interests

My research focusses on problems in geometry related to wall-crossing phenomena observed in mathematical physics. In particular I am interested in spaces of stability conditions on triangulated categories, a geometric invariant of a triangulated category with walls along which the class of stable objects jumps. Most of the articles below can be found on my arXiv page.

Research articles

Theses

  • Stability conditions and Seiberg-Witten quivers (2014, PhD thesis, University of Sheffield)

    This generalises the techniques of the above article on the A2 quiver to describe a connected component of the space of numerical stability conditions on the Calabi-Yau-3 triangulated categories associated to finite and affine Dynkin diagrams whose Cartan matrix is of rank 2. This class of triangulated categories arises in the geometric engineering of the asymptotically free SU(2) Seiberg-Witten theories and their degenerations into Argryes-Douglas theories. They are also in bijection with the Painlevé equations which define the isomonodromic deformations of the corresponding moduli spaces of flat connections studied in Gaiotto-Moore-Neitzke.

  • Etale cohomology (2008, Part III Essay, University of Cambridge)

    This is an introduction to étale cohomology written whilst a was a Part III (Master's) student at the University of Cambridge. As with many Part III essays it was written in a very short space of time whilst the material on which it is based was all very new to me. I put it here not because it is a clear, well-written, error-free survey (it is not), but it might give some idea of what a Part III essay is like.