Research Interests

A (possibly slightly outdated) comprehensive research statement can be found here.

A brief overview:

Broadly speaking, I am interested in problems with a number theoretical flavor, often lying in the intersection of number theory with (complex) analysis and/or model theory.

My PhD topic falls under the umbrella term "arithmetic properties of transcendental functions". More specifically, we focused on counting rational (or algebraic) points of bounded height and degree on graphs of analytic or meromorphic functions, the latter for which we adopted a Nevanlinna theoretic approach.

Of late my interests are leaning towards the interactions of model theory with (transcendental) number theory and analysis. In particular, I am interested in questions around exponential transcendence as well as arithmetic properties of sets definable in certain expansions of the real field.

I am also interested in Diophantine problems involving linear recurrent sequences. This often involves the application of Baker's theorem on linear forms in logarithms to obtain finiteness results for solutions of such equations.

As part of my MSc, I worked on the "geometry of complex polynomials". The general theme of the area is to study the location of critical points of polynomials relative to their zeroes. More specifically, we worked on Sendov's Conjecture.

Publications/Preprints (Oldest to newest):

  1. Sendov's conjecture: On a paper of Degot. Analysis Mathematica.

  2. Algebraic values of certain analytic functions defined by a canonical product. B. Aust. Math. Soc.

  3. Algebraic values of entire functions with extremal growth orders: An extension of a theorem of Boxall and Jones. Canad. Math. Bull.

  4. Nevanlinna theory and algebraic values of meromorphic functions. International Journal of Number Theory.

  5. Padovan numbers which are palindromic concatenations of two distinct repdigits. (with M Ddamulira), submitted. Accepted.

  6. Perrin numbers as concatenations of two repdigits. (with M Ddamulira), submitted. Preprint.

  7. On algebraic values of Weierstrass $\sigma$-functions. (With Gareth Boxall and Gareth Jones), submitted. Preprint.

  8. Algebraic independence of values of the $p$-adic Euler factorial series. (With Andry Rabenantoandro). In preparation.

  9. A continuous homomorphism of a thin set onto a fat set. (With Sidney A. Morris). Submitted.

  10. Topological transcendental fields. (With Sidney A. Morris). Axioms.

  11. Erdos-Liouville sets. (With Sidney A. Morris). In preparation.