Vidnyánszky Zoltán: The theory of Borel equivalence relations

One of the central themes of descriptive set theory is the study of definable equivalence relations—particularly Borel and analytic ones—and their hierarchy under Borel reducibility. In this talk, I will survey the area, highlighting several fundamental results and major open problems. I will discuss applications and why this line of research is of interest to mathematicians outside descriptive set theory. In the final part of the talk, I will focus on questions that I find particularly intriguing concerning the notion of hyperfiniteness.