Bachelor and master projects
Possible projects (not exhaustive)
Differential geometry
- Thurston's earthquake theory for surfaces
- Selberg trace formulas and the like
Algebraic geometry
- Arithmetic aspects of topological recursion
- Exploring intersection numbers on the moduli space of curves
- Deformation spaces of spectral curves and Frobenius manifolds
Mathematical physics
- Enumeration of branched covers of curves (Hurwitz theory) and integrability
- Airy structures, topological recursion and topological gravity
- Algebraic structures in low-dimensional TQFTs
Analysis
- Determinantal structures and vanishing properties in matrix ODEs
Current projects
Mathematical physics
Florian Götz (HU, Master): Spectral networks and the geometry of surfaces
Niklas Martensen (HU, Master): Modular properties of the topological recursion
Analysis and combinatorics
Bianca Drefahl (HU, Bachelor): Modular q-difference equations
Former projects
Mathematical physics
Thomas Buc d'Alche (ENS Lyon, Master): Pfaff-Fay identities via asymptotics of random matrices
Ines Combes-Castex (Univ. Toulouse, Bachelor): Matrix models as a toy model for QFT