Some of our research interests include:
- Moduli spaces of curves and abelian varieties, tautological classes, Siegel and Teichmüller modular forms, and their relation to the cohomology of moduli spaces, linear orbits of plane curves
- Arithmetic geometry and algebraic number theory, rational points of algebraic varieties, zeta functions and Galois representations associated to algebraic varieties
- Moduli spaces of sheaves, (virtual) enumerative geometry on 2-, 3-, and (Calabi-Yau) 4-folds, Donaldson-Thomas and related invariants, relations to combinatorics, modular forms, and theoretical physics
- Diophantine geometry, arithmetic applications of birational geometry, varieties over non-algebraically closed fields, Cox rings, Fano varieties, toric varieties, rationally connected varieties, rational points over global fields
Our members are part of the Dutch clusters Discrete, Interactive and Algorithmic Mathematics, Algebra and Number Theory (DIAMANT) and Geometry and Quantum Theory (GQT).
Dirk van Bree (webpage)
Supervisor: Martijn Kool
Interests: Moduli space of sheaves and complexes
Mar Curcó Iranzo (webpage)
Supervisor: Valentijn Karemaker
Interests: Arithmetic geometry and number theory: Rational points on Jacobians of modular curves, modular forms and elliptic K3 surfaces.
Supervisor: Carel Faber
Carel Faber (webpage)
Interests: Algebraic geometry (moduli spaces of curves and of abelian varieties, tautological classes, Siegel and Teichmüller modular forms and their relation to the cohomology of moduli spaces, linear orbits of plane curves).
Valentijn Karemaker (webpage)
Interests: Arithmetic geometry and number theory: rational points on, zeta functions of, and Galois representations attached to algebraic varieties.
Martijn Kool (webpage)
Interests: Algebraic geometry. Moduli spaces of sheaves on toric varieties. Stable pair invariants and their connections with enumerative geometry.
Stefano Marseglia (webpage)
Interests: Arithmetic Geometry and Number Theory, with focus on computational aspects
Boaz Moerman (webpage)
Supervisor: Marta Pieropan
Interests: Number theory and algebraic geometry: rational points, L-functions, modular forms.
Supervisor: Martijn Kool
Marta Pieropan (webpage)
Interests: algebraic geometry and number theory, Diophantine geometry, analytic number theory
Counting sheaves on Calabi-Yau 4-folds. Seminar on a recent preprint of Oh-Thomas on the construction of virtual structures on moduli spaces of coherent sheaves.