A positive dichotomy between frieze patterns and Diophantine geometry

讲座题目：A positive dichotomy between frieze patterns and Diophantine geometry
讲座时间 Datetime: 2025年06月12日，周四， 10:30—11:30
地点 Venue: 海琴二号楼A412
主持人 Host：黄敏 副教授
报告人 Speaker: Robin Zhang 博士
单位 Affiliation: 麻省理工大学
报告摘要 Abstract:
This talk will highlight how recent work by Antoine de Saint Germain, Min Huang, and Jiang-Hua Lu can be used to bridge cluster algebra theory and number theory. First, I will describe how arithmetic geometry can be used to enumerate positive integral friezes of any given Dynkin type, including E7 and E8 which are the subjects of the Fontaine–Plamondon conjecture. Second, I will describe the converse: how friezes are remarkable sources of infinitude for positive integral points in Diophantine geometry, including surfaces and threefolds studied by Mordell and Schinzel. Hopefully, this also opens a number theoretic line of investigation into questions about friezes in more general rings of integers and integral domains – or the converse!
报告人简介：
Robin Zhang现任美国麻省理工大学NSF Postdoctoral Fellow，他2023年5月于美国哥伦比亚大学取得博士学位，导师为著名数学家Michael Harris教授。Robin Zhang主要从事数论、自守表示以及丢翻图几何等方向的研究，部分研究成果目前已发表于Int. Math. Res. Not. ，Math. Res. Lett.，Annales de l'Institut Fourier等多个国际期刊。