Research interests

I have been trained as a mathematical logician, with focus in set theory. My research interests currently lie in descriptive set theory and its applications to other fields of mathematics such as topological dynamics and group theory. That said, I am also interested in various questions of more pure set-theoretic nature.

Descriptive set theory, in the broadest sense, is the study of “definable” subsets of Polish spaces. For a detailed discussion of how classical descriptive set theory came into existence, you can read this excellent article by Akihiro Kanamori.

As it is the case with any other field of mathematics, descriptive set theory has evolved over time. One of the major research areas of contemporary descriptive set theory is the study of Borel equivalence relations. Although the study of Borel equivalence relations is important on its own and has its own motivations, it also provides a mathematical framework to analyze the relative complexity of classification problems from diverse areas of mathematics.

My PhD dissertation was about the analysis of some classification problems from topological dynamics. More specifically, I analyzed the Borel complexity of the topological conjugacy relation on various Cantor minimal systems, including certain symbolic systems. Since then, I have been working on some problems regarding hyperfinite Borel equivalence relations and some problems in group theory of model-theoretic nature.