معرفی
Dr. Yurii Khomskii holds multiple academic positions across European institutions. He serves as a Lecturer and Academic Tutor at Amsterdam University College, a Privatdozent (equivalent to Senior Lecturer/Associate Professor) in the Department of Mathematics at Universität Hamburg, and a Guest Researcher at the Institute of Logic, Language and Computation (ILLC) at the University of Amsterdam. His work bridges mathematical logic, set theory, and foundations of mathematics across these institutions.
Dr. Khomskii obtained his PhD from the University of Amsterdam in 2012 under the supervision of Prof. Benedikt Löwe and Prof. Jörg Brendle, with a dissertation titled Regularity Properties and Definability in the Real Number Continuum. He completed his Habilitation at Hamburg University in 2018 with the work Cardinal Characteristics, Regularity Properties, Definability and the Structure of the Real Line and the Generalised Real Line. Prior to these achievements, he held postdoctoral positions at the Kurt Gödel Research Center for Mathematical Logic at the University of Vienna and Universität Hamburg, and was a Marie Sklodowska-Curie research fellow.
His research focuses on mathematical logic and set theory, specifically exploring the structure of the real line, regularity properties of sets of reals, descriptive set theory, forcing techniques, and generalized real numbers and Baire spaces. His work combines deep theoretical investigations with connections to foundational questions in mathematics. Dr. Khomskii's approach often involves analyzing cardinal characteristics, investigating definability constraints, and examining the interplay between combinatorial principles and regularity properties in various set-theoretic contexts.
Analysis of his recent publications reveals a consistent trajectory in advanced set theory, with increasing focus on generalized Baire spaces and alternative set-theoretic frameworks. His work spans from concrete investigations of cardinal characteristics and regularity properties to more foundational explorations of paraconsistent and paracomplete set theories. The evolution shows a progression from classical descriptive set theory toward more abstract and generalized frameworks, while maintaining rigorous mathematical standards.
Dr. Khomskii has been actively involved in teaching and mentoring across multiple institutions. He regularly coordinates intensive projects at the ILLC on advanced topics in set theory, forcing, and mathematical logic. At Universität Hamburg, he guides student seminars on logic and set theory topics. His teaching spans foundational courses like propositional logic and Boolean algebras to advanced topics such as infinite games, forcing, and generalized Baire spaces. He has supervised numerous student projects and coordinated semester-long intensive courses that combine theoretical instruction with practical problem-solving sessions.
His research activities include directing student projects like the 2023 Forcing and Independence Proofs coordinated project at ILLC, where students explored forcing techniques and independence proofs in set theory. He has also led seminars on topics including infinite computability, descriptive set theory, and advanced set theory at both Universität Hamburg and the ILLC. His research collaborations span across Europe, with frequent co-authorships with researchers from Vienna, Amsterdam, and other mathematical logic centers.
