Yurii obtained his PhD at the University of Amsterdam in 2012. After that, he held a postdoctoral position at the University of Vienna, Austria, and was a Marie-Sklodowska-Curie research fellow at Hamburg University, Germany, where he also obtained the Habilitation (post-doctoral degree).

He has been teaching at AUC since 2019. Outside of AUC, he is permanently affiliated with Hamburg University as Privatdozent, where he regularly visits and coordinates projects and seminars. 

Yurii Khomskii is an active researcher in logic and axiomatic set theory, an area of mathematics dealing with foundational questions on the nature of mathematical objects, the language of mathematics and the limitations of mathematical provability. His work focuses on the foundations of the real number continuum, generalisations to spaces of higher cardinality, and applications to analysis and other areas of mathematics. He is a guest researcher at the Institute of Logic, Language and Computation (ILLC) at the University of Amsterdam.