Research

A. Hodge Theory and topology of algebraic varieties

• Cycles on abelian varieties

• Ball quotients and fibre bundles over the circle

• Combinatorial and topological aspects of hyperplane arrangements

• Hyperplane arrangements, cubic curves and algebraic surfaces

• Sheaves on abelian varieties

B. Geometry and combinatorics of moduli

• Uniformization of moduli of abelian varieties

• Curves and K3 surfaces

• Positivity on moduli spaces of curves

• (Birational) Automorphisms of Calabi-Yau varieties and the cone conjecture

• Hurwitz theory, cohomological field theories and geometry of moduli spaces

• Reflection groups, monodromy and cluster algebras

C. Rational points and the arithmetic of moduli

• Counting rational points on curves and surfaces

• Cox rings of algebraic surfaces

• Arithmetic points for the moduli of curves

• Integral points on moduli, period maps and Tannakian methods