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, 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, an extremely general theory whose objects of study are the abstract infinite sets. 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 virtually all of mathematics can be formally reduced to it. I help to develop and apply sophisticated techniques, such as Forcing and Large Cardinals, towards the solution of hard problems in Set Theory itself and in other areas of logic and mathematics. More interestingly, it is sometimes possible to prove 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, Magidor M & Mancilla S 2020, 'The consistency strength of hyperstationarity'. Journal of Math. Logic. Vol. 20, No. 01, 2050004.

Selected research activities

Invited speaker: Structural Reflection: from Strong to Woodin cardinals. Catania Set Theory and Topology Conference. Catania (Italy). 18-21 February 2020.

Invited talk: From Strong to Woodin cardinals. A level-by-level analysis of the Weak Vopenka principle. CUNY Set Theory Seminar (Online). 1 May 2020.

PhD Thesis supervisor: Alejandro Poveda. Contributions to the theory of Large Cardinals through the method of Forcing. Universitat de Barcelona, Faculty of Mathematics. Graduation date: 9 November 2020. Qualification : Excellent cum laude. Current position: Postdoctoral researcher at Einstein Institute of Mathematics, Hebrew University (Jerusalem).

Master Thesis supervisor: Fernando Barrera, Usuba's contributions to set-theoretic geology. Curial Gallart, Cardinal Arithmetic: from Silver's Theorem to Shelah's PCF Theory. John Spoerl, Cardinals Beyond Choice and the HOD-Dichotomy.

PhD fellow supervisor: Zhixing You, Chinese Academy of Sciences (Beijing). PhD Joint Training program. Project: Some problems about large cardinals.

Postdoctoral fellows supervisor: Philipp Lücke (U. Bonn). Marie Sklodowska Curie Postdoctoral Grant (EU). Period: 2 years, starting in April 2020. Project: Strong Axioms of Infinity: Frameworks, Interactions and Applications. Claudio Ternullo (Rome). Beatriu de Pinós Postdoctoral Grant (Catalan Government). Period: 3 years starting in February 2020. Project: Mathematical and Philosophical Aspects of a Multiversist Foundations of Set Theory.