时间：2025年6月19日（星期四）15:00-16:00
地点：西湖大学云谷校区E4-233
主讲人：Robin Zhang, MIT
报告题目：A positive dichotomy between Diophantine geometry and Dynkin frieze patterns
报告摘要：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.
