Research
What is it about?
The focus of most of my research is the model theory of fields. Usually (but not always) this means exponential fields or valued fields.
On the side of exponential fields I am mostly interested in Zilber's conjectures predicting that the complex exponential field is quasiminimal and exponentially-algebraically closed.
On the side of valued fields, I am interested in the connections between model theory and tropical geometry.
Publications and preprints
- "Exponential sums equations and tropical geometry", Selecta Mathematica (New Series), 29(49), 2023.
- "Dividing lines between positive theories" (with Anna Dmitrieva and Mark Kamsma), Journal of Symbolic Logic, published online 2023.
- "On some systems of equations in abelian varieties", International Mathematics Research Notices, 2024(9), 2024.
- "Quasiminimality of complex powers" (with Jonathan Kirby), Forum of Mathematics, Sigma , 12(e123) , 2024.
- "Solving systems of equations of raising-to-powers type", Israel Journal of Mathematics (to appear).
- "The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations" (with Stefano Mereta), submitted.
- "Exponential sums equations and the Exponential Closedness conjecture" (with Vahagn Aslanyan), submitted.
- "Projective curves and weak second-order logic" (with Alessandro Berarducci), submitted.
PhD Thesis
I wrote my PhD thesis, "Around Exponential-Algebraic Closedness", between 2018 and 2022 at the University of Leeds, under the supervision of Vincenzo Mantova. It is about, well, Exponential-Algebraic Closedness, and it contains roughly the same things as papers 1, 3, and 5 listed above (although I would recommend looking at the papers), together with a general introduction to the problem and some of the further directions of research that I cared about as of April 2022.