My research mostly lies in mathematical logic, set theory and the applications of logic in other areas of mathematics.In this work, I study axioms of strong infinities, forcing, set-theoretic definability, infinitary combinatorics and automorphism groups of large structures. Much of my research is motivated by the ubiquity of independence results in set theory and the resulting search for intrinsically justified new axioms for mathematics that provide answers to the great variety of questions from various fields of research that are left open by the current standard axiomatization of mathematics.