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I am a researcher in mathematics at the IMB and I work in number theory at large, especially in Diophantine geometry. I have previously held postdoctoral positions at Sorbonne University and Grenoble Alpes University. I obtained my PhD in 2022 under the supervision of Yuri Bilu. I am most interested in unlikely intersections, André–Oort theorems, complex multiplication and singular moduli, intersection problems in algebraic groups, division fields and Artin’s conjecture.
Publications ⯆
Research ⯆
- Effective unlikely intersections in Shimura varieties. Not all points in Shimura varieties, like the modular curve that parametrizes elliptic curves up to isomorphism, are created equal, and of special interest are their “special” points and subvarieties. Special subvarieties determine the geometry of the ambient variety in a powerful way. However, there is no way in general that one can do so effectively, i.e. in a way that a computer can certifiably enumerate. I work on making this possible in concrete instances, using strong properties of the j-invariant.
- Arithmetic statistics in algebraic groups. A GCD between two numbers can be interpreted as an intersection of certain geometric objects attached to them. One can then study the behavior of this intersection in orbits within algebraic groups, the simplest instance being the question: are there infinitely many n such that gcd(2n-1,3n-1)=1? This is connected to surprisingly many topics, like Diophantine error terms and the Subspace theorem, Kummer theory and Artin's primitive root conjecture, and the arithmetic of algebraic groups; I proved some cases of it.
- Integer approximation theory and capacity. Chebyshev’s famous theorem characterizes normalized polynomials (with leading cofficient 1 and rational coefficients) of minimal supremum norm on an interval. What if we instead drop the normalization and ask that the polynomials have integer coefficients—but no longer be monic? This is a deep unsolved problem with its roots in approximation theory and potentials.
Useful links. L-functions and modular forms, Stacks project, Universe of theories.
Other. Check out my grandpa’s collected works and internment memories.
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