In this talk, we will examine variants of sequential compactness and countable compactness that are associated with Ramsey-like properties. These notions have arisen naturally in various topological and combinatorial contexts. We will present several results obtained by treating these compactness properties as central objects of study. The talk will conclude with some connections to classical problems and open questions.

Slides: https://drive.google.com/file/d/1ZUkSXkjsNPIVzm1JHAJmBVttklcd_Atg/view?usp=drive_link