Hindman’s Theorem

讲座题目：Hindman’s Theorem
讲座时间 Datetime:2026年10月16日， 周五， 08：00 -11：00
地点 Venue: 海琴二号A412-1
主持人 Host：Sergio Romana  副教授
报告人 Speaker:  Jonatas Marinho Santos de Araujo 博士
单位 Affiliation: National Institute of Pure and Applied Mathematics - IMPA
报告摘要 Abstract: 
The classical theorem of Hindman is a theorem regarding the existence of a set of infinite partial sums of an infinite set (IP sets) in a member of a finite partition. In this talk, we aim to present a proof based on ultrafilters, which is due to Galvin and Glazer.
We comment on how IP sets appear naturally in the context of recurrence in Ergodic Theory. We introduce and comment on ultrafilters, their structures, and demonstrate how the existence of an idempotent ultrafilter implies the theorem.
报告人简介：
Jonatas Marinho Santos de Araujo is a PhD student at the National Institute of Pure and Applied Mathematics (IMPA), Brazil, working in the field of dynamical systems. He is currently a visiting scholar at the School of Mathematics (Zhuhai), Sun Yat-sen University, where she is completing a six-month academic research collaboration with the Dynamical Systems Group.