Joan Bagaria

Joan Bagaria

Universitat de Barcelona

Experimental Sciences & Mathematics

Born on 17 August 1958 in Manlleu (Catalonia). Fulbright Fellow at Univ. of California, Berkeley, 1985-87. PhD in Logic and the Methodology of Science, UC Berkeley, 1991. Postdoctoral researcher, UC Berkeley, 1991-92. Associate Professor at several Catalonian universities, 1992-2001. ICREA Research Professor at Univ. of Barcelona, since 2001. Invited researcher at UC Berkeley, Kobe Univ., National Univ. of Singapore, Kurt Gödel Research Center (Vienna), Univ. Paris VII, CalTech, Mittag-Leffler Institut, Hebrew Univ., Harvard Univ., etc. First President of the European Set Theory Society, 2007-11; ICREA Director's Scientific Advisor, since 2005; Chairman of the INFTY ESF-Research Networking Programme, 2009-14; Simons Foundation Fellow at Isaac Newton Institute, University of Cambridge, UK, Aug. to Dec. 2015. Director of the Barcelona Research Group on Set Theory (BCNSETS), and coordinator and PI of the UB-based Barcelona Logic Group (BCNLOGIC).

Research interests

I am a mathematical logician working mainly in Set Theory. Set Theory is the strongest and most encompassing of mathematical theories. It is both the theory of infinity and the standard foundation for mathematics, in the sense that all of mathematics can be interpreted and formally reduced to it. I develop sophisticated techniques, such as the method of Forcing for building models of Set Theory and the theory of Large Cardinals, and apply them to the solution of hard problems in Set Theory itself and in other areas of logic and mathematics. Most  interestingly, one can prove sometimes that a given problem cannot be solved using standard mathematical tools, which are embodied in the standard Zermelo-Fraenkel with Choice (ZFC) axioms of Set Theory, and therefore new axioms are needed for its solution. Finding and classifying new axioms, thereby expanding the frontiers of mathematical reasoning, is also an essential part of Set Theory, and of my work.

Selected publications

- Bagaria J & Wilson TM 2022, ‘The Weak Vopenka Principle for definable classes of structures'. The Journal of Symbolic Logic, 88, 1, 145 - 168, PII S0022481222000421.

Selected research activities

Invited speaker. Large cardinals in set theory and beyond. Recent advances in Mathematics and related areas. Kerala School of Mathematics. Kozhikode, Kerala, India (Online). 21-24 April 2022.

Chairman of the Program Committee. European Set Theory Conference (ESTC). August 29-September 2, 2022. Torino (Italy).

Member of the Joint Editorial Board of the Bulletin and the Journal of the London Mathematical Society. Since January 2022.

PhD Thesis co-supervisor of Zhixing You (PhD joint training program, Chinese Academy of Sciences, Beijing. Co-supervised with Prof. Liuzhen Wu). Title of dissertation: On the delta-strong compactness. Graduation date: 30 June 2022. Qualification : Outstanding. Current position: Postdoctoral Fellow (with Asaf Rinot), Bar-Ilan University, Israel.