Welcome to my teaching and research site

I am an Assistant Professor at the University of Warwick.  Previously I have been a PostDoc at the University of Basel and a research associate at the University of Manchester. Before that I was a Phd student at the University of Basel under the supervision of David Masser and a SNF-fellow at the University of Oxford. 

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Interests: My main interest lies in Diophantine Geometry, which I would define as the study of number theoretic questions in connection with or the help of algebraic geometry, algebraic groups, heights, special functions, transcendence and equidistribution. A lot of what I am interested in is described in books of Lang, Hindry and Silverman as well as Bombieri and Gubler (to name a few). In recent years I have become increasingly interested in the arithmetic of dynamical systems.  

Unlikely intersections: An umbrella term for almost all of what I am interested in is unlikely intersections. This term most likely originates from work of Enrico Bombieri, David Masser and Umberto Zannier at the end of then 1990's and describes a principle that unites different branches of mathematics such as logic, algebraic geometry, dynamical systems and Diophantine geometry. Precise conjectures by Boris Zilber and by Richard Pink fall under this umbrella term and show the power of the underlying principle.  In recent years, it has become apparent that this principle also rules in algebraic dynamical systems and that it can be used to formulate precise conjectures there. 

The principle of unlikely intersections can be summarised as  follows. Two ``varieties" in an underlying space ``should not" intersect if their dimensions do not add up to the dimension of the underlying space. Even if we take a countable union of such intersections, where this countable union is defined in terms of the geometry of the underlying space, the resulting union should be describable in finite terms.  

Effectivity: Part of my work has been concerned with finding effective proofs. In computational terms, the task is to find an algorithm that solves the problem instead of describing it qualitatively. For example, instead of knowing that the solution set of a given Diophantine equation is finite, we would like to be able to compute all solutions. It is clear since work of Matiyasewitch and Robinson that there can't be a ``universal" algorithm that solves Diophantine equations.