Bachelor and master projects
Possible projects (not exhaustive)
Differential geometry
- Thurston's earthquake theory for surfaces
- Selberg trace formulas and the like
- Compactifications of the moduli space of complex curves
Algebraic geometry
- Arithmetic aspects of topological recursion
- Exploring intersection numbers on the moduli space of curves
- Deformation spaces of spectral curves and Frobenius manifolds
- Cohomological field theories and Teleman reconstruction theorem
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
- Matrix factorisations and enumerative geometry
- W-algebras and r-spin intersection numbers
Analysis and combinatorics
- Determinantal structures and vanishing properties in matrix ODEs
- Asymptotic questions in large random matrices
- Representation theory of U(N) and coupled random matrices
- Free probability and random matrices
Ongoing projects
Mathematical physics
Niklas Martensen (Master)
Modular properties of the topological recursion
Dominik Stepien (Bachelor)
Finite-dimensional Airy structures
Leonard Vetter (Bachelor)
Algebraic structures and TQFTs
Analysis and combinatorics
Bianca Drefahl (HU, Bachelor)
Modular q-difference equations
Former projects
Florian Götz (HU, Master), defended January 2022
Spectral networks and the geometry of surfaces
Thomas Buc-d'Alché (ENS Lyon, Master)
Pfaff-Fay identities via asymptotics of random matrices
Inès Combes-Castex (Univ. Toulouse, Bachelor)
Matrix models as a toy model for QFT