Changes in arithmetic properties of rational points of some curves with respect to field extensionsMPIM

by Sun Woo Park (MPIM)

Thursday Jun 25, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

Finding solutions of a polynomial equation $f(x,y) = 0$ over the rational numbers $\mathbb{Q}$ (such as Fermat's last theorem) has been one of the key classical problems in number theory. A related question is to ask whether the number of solutions (or other arithmetic properties) changes if we find solutions to the same equation over an extension field, such as $\mathbb{Q}(i)$ or $\mathbb{Q}(\sqrt{5})$. We will discuss some of the quantitative characterizations of changes in arithmetic properties of solutions to these polynomial equations. If time allows, we will discuss how such characterizations hint at a possible interplay among arithmetic statistics of rational points on curves, stochastic properties of Markov operators, and topological properties of Hurwitz spaces. The talk is based on joint works with Daniel Keliher, Stevan Gajovic, and Wanlin Li, as well as some other works of mine.