Between 2019—2022 I was an RTG Postdoctoral scholar and Unit 18 Lecturer at UC Berkeley, working in the Arithmetic Geometry group.
I did my DPhil at the University of Oxford under the supervision of Jonathan Pila. The title of my thesis: Model Theory of Shimura Varieties. Graduated in 2019.
I did my Master at Pontificia Universidad Católica de Chile under the supervision of Giancarlo Urzúa. The title of my thesis: Logarithmic Chern Slopes of Arrangements of Rational Sections in Hirzebruch Surfaces. Graduated in 2015
I am interested in the interactions between model theory, number theory and algebraic geometry.
Right now, I am focused on studying various open problems related to the interaction between arithmetic and geometry such as the Existential Closedness problem, the Grothendieck-André generalised period conjecture, the Mumford-Tate conjecture, and the Zilber-Pink conjecture. These questions arise somewhat naturally when one is trying to understand the algebraic properties of important transcendental functions in arithmetic geometry.
For example, for the complex exponential function there are still various open problems concerning its algebraic properties: whether or not e and π are algebraically independent, the four exponentials conjecture, Schanuel's conjecture; among others. Since these questions have proven to be very hard to solve, it is natural to study how they relate to each other.
A major motivation of my work is Boris Zilber's results on pseudo-exponentiation (further studied and completed by Martin Bays and Jonathan Kirby, among others), which conjectures a precise algebraic axiomatisation for the exponential function. Among the axioms, there are instances of the conjectures mentioned above.<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>
- DPhil in Mathematics, University of Oxford
Research groups and institutes