Our research encompasses a broad range of topics within number theory. Some of our research interests include:

- Algebraic curves
- Algebraic and arithmetic dynamics
- Algorithmic number theory
- Analytic number theory
- Applications of number theory to spectral geometry
- Arithmetic geometry
- Arithmetic of linear differential equations
- Arithmetic statistics
- Diophantine problems
- Geometry of numbers
- Hypergeometric functions
- Number theory in function fields of positive characteristic
- Relation between number theory and logic: undecidability and o-minimality

Our members are part of the Dutch clusters on Discrete, Interactive and Algorithmic Mathematics, Algebra and Number Theory (DIAMANT) and Geometry and Quantum Theory (GQT).

#### Our members

**Johan Commelin**(webpage)

Interests: formalization of mathematics, arithmetic geometry, o-minimal theory, categorical logic, type theory

**Gunther Cornelissen**(webpage)

Interests: Number Theory and Geometry

**Valentijn Karemaker**(webpage)

Interests: Arithmetic geometry and number theory: rational points on, zeta functions of, and Galois representations attached to algebraic varieties.

**Marta Pieropan**(webpage)

Interests: algebraic geometry and number theory, Diophantine geometry, analytic number theory

**Lola Thompson**(webpage)

Interests: Analytic number theory, algorithmic number theory, applications of number theory to spectral geometry

**Stefano Marseglia**(webpage)

Interests: Arithmetic Geometry and Number Theory, with focus on computational aspects

**Sara Mehidi**(webpage)

Interests: Algebraic geometry and logarithmic geometry and their applications to arithmetics

**Soumya Sankar**(webpage)

Interests: Arithmetic geometry, rational points on varieties and stacks, moduli spaces, curves and abelian varieties, obstruction problems.

**Sebastián Carrillo Santana**(webpage)

Supervisor: Lola Thompson

Interests: Analytic number theory, modular forms and sieve methods

**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.

**Samira le Grand**

Supervisor: Lola Thompson

Interests: Applications of number theory to spectral geometry

**David Hokken**(webpage)

Supervisor: Gunther Cornelissen & Lola Thompson

Interests: Number theory, in particular zeroes/Galois theory/complex dynamics of Littlewood polynomials

**Boaz Moerman**(webpage)

Supervisor: Marta Pieropan

Interests: Number theory and algebraic geometry: rational points, L-functions, modular forms.

**Justin Uhlemann**

Supervisor: Marta Pieropan

Interests: Arithmetic geometry and analytic number theory: Points of bounded height, local-global principles

**Hsin-Yi Yang**

Supervisor: Valentijn Karemaker

Interests: Algebraic number theory and abelian varieties

#### Emeritus staff

**Frits Beukers**(webpage)

Interests: Number theory (in particular diophantine matters), Arithmetic and monodromy of linear differential equations, hypergeometric functions.

**Roelof W. Bruggeman**(webpage)

Interests: Automorphic forms.

**Frans Oort**(webpage)

Interests: Algebraic geometry, arithmetic algebraic geometry, moduli of abelian varieties in positive characteristic.