Time：10:00-12:00, Wednesday, June 18 2025
Venue：E4-233
Speaker：Robin Zhang, MIT
Title：A positive dichotomy between Diophantine geometry and Dynkin frieze patterns
Abstract：General finiteness results for positive integer solutions to Diophantine equations are rare. In this talk, I will describe how the theory of cluster algebras can be a remarkable source of finiteness & infinitude in the form of a Siegel theorem for positive integral points on affine varieties of dimension at least 2. On the finiteness of positive integral points, I will highlight 7-dimensional and 8-dimensional affine varieties that arise in the proof of the Fontaine–Plamondon conjecture for Dynkin friezes. On the infinitude of positive integral points, I will highlight surfaces and threefolds that arise in the Mordell–Schinzel program.
