Research

The main focus of my research is the study of Galois representations.

I am interested in the interplay between representation theory, number theory and arithmetic geometry.

In my research I am following ideas which benefit from connections between different areas of mathematics: discrete mathematics, graph theory, lattice theory, algebraic geometry, as well as arithmetic geometry, algebra and number theory.

In particular, some of my research projects include algorithmic aspects and extensive computations using various computer algebra systems (SageMath, Magma and PARI/GP).

Currently, I am investigating congruences between modular forms and questions regarding the inverse Galois problem for representations attached to torsion subgroups of abelian varieties.

I am also constructing several databases (see my my github repositories) and I am a member of the LMFDB Collaboration.