Research Focus
Research Area: Arithmetic Geometry, especially arithmetic fundamental groups and Chabauty—Kim theory
One of the oldest kinds of problems in number theory are Diophantine equations, famous examples of which include the Pythagorean equation, the Pell equation, and the Fermat equation, famously solved at the end of the last century by Wiles and Taylor. I am interested in a modern perspective on these kinds of problems, in which one studies the shape cut out by a Diophantine equation using tools from algebraic topology. My work applies these tools to problems including counting the number of solutions to Diophantine equations, and developing and improving methods for solving them in practice, especially the Chabauty—Kim method.
Publications
- (with J. Duque-Rosero, S. Hashimoto and P. Spelier) Local heights on hyperelliptic curves and quadratic Chabauty. arXiv:2401.05228
- (with J. Stix) Galois sections and p-adic period mappings. To appear in Ann. of Math., arXiv:2204.13674.
- (with A.J. Best, T. Kumpitsch, M. Lüdtke, A.W. McAndrew, L. Qian, E. Studnia and Y. Xu) Refined Selmer equations for the thrice-punctured line in depth two. Math. Comp. 93, pp. 1497–1527.
- Weight filtrations on Selmer schemes and the effective Chabauty–Kim method. Compos. Math., 159(7), pp.
1531–1605.