Hello! I earned my PhD from TU Graz. My dissertation was, “Introduction to Hecke vector-forms: a generalized automorphic form as a vector over a Hecke triangle group.” I developed the elements of a theory for a new class of vector functions called Hecke vector-forms. These transform like automorphic forms on an arbitrary Hecke triangle group and thus are a natural extension of this very classical topic. Notably, these underlying Hecke groups appear in a variety of places from number theory to knot theory, and so we expect these functions to have a wide variety of uses as they become better understood.
More generally, projects that I like tend to come from arithmetic, though landing at the junction of many theories (say, e.g. statistical mechanics and conformal geometry). Tools I like come from differential equations (linear and non-linear), special functions, matrix theory, geometry, and complex analysis. I am always looking for arithmetic problems that require a healthy combination of these techniques.
That said, I am fond of many aspects of the Hardy-Littlewood school of “hard” analysis; in contrast, I typically do not work in theories that generalize away many valuable details. I have an Erdös number 3 (if you’re amused by that sort of thing) via Professor Victor Moll at Tulane University. Thank you for visiting my professional site!
Michael Andrew Henry 