Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

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