Hello and welcome to my research page!
I recieved my PhD from TU Graz in Austria. In my dissertation project (advised by Peter J. Grabner), I define an analytic mapping from an arbitrary quasiautomorphic form (modulo any Hecke triangle group) to a vector-valued automorphic form: under this precise mapping we call these functions Hecke vector-forms. In a recent preprint, I extended this mapping to a bijection between quasiautomorphic forms and Hecke vector-forms.
In general this research is aimed towards developing a fully explicit theory of vector-valued automorphic forms, but not just over the Hecke triangle groups: the goal is a functional theory over all Schwarz triangle groups, including arithmetic and non-arithmetic groups alike.
We want to do this because the Schwarz triangle groups (and their subgroups) are essential to a complete understanding of algebraic curves; this we know because Belyi’s theorem has a triangle group formulation. For more information on the connections between triangle group geometry and algebraic curves, see the fascinating book here.
