ICREA Research Professor at Univ. of Barcelona. Invited researcher at UC Berkeley, Kobe Univ., National Univ. of Singapore, Kurt Gödel Research Center (Vienna), Univ. Paris VII, CalTech, Mittag-LefflerInstitut, Hebrew Univ., Harvard Univ., Isaac Newton Institute (Cambridge), 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; Member of the Standing Committee of the Catalan Counsel for the Communication of Science (C4). Director of the Barcelona research group on set theory (BCNSETS). I have written over 40 research and survey papers on set theory and its applications to other areas of mathematics.
- Set Theory (large cardinals, forcing, infinite combinatorics, descriptive set theory)
- Mathematical Logic
- Foundations of Mathematics
- Philosophy of Mathematics
- Bagaria Joan, CasacubertaCarles, Mathias A.R.D., RosickýJiří: Definable orthogonality classes in accessible categories are small. J. Eur. Math. Soc. 17 (2015), 549-589.doi: 10.4171/JEMS/511.
- Bagaria, J.; Magidor, M., Group radicals and strongly compact cardinals. Transactions of the American Mathematical Society.366 (2014), 1857-1877.
- Bagaria, J.; Magidor, M., On $\omega_1$-strongly compact cardinals.The Journal of Symbolic Logic.Volume 79 / Issue 01 / March 2014, pp 266-278.
- Bagaria, J., C(n)-cardinals. Archive for Mathematical Logic, Arch. Math. Logic (2012) 51:213-240. DOI 10.1007/s00153-011-0261-8.
- Bagaria, J., Set Theory. Princeton Companion to Mathematics. Timothy Gowers, June Barrow-Green, and Imre Leader, Editors. Princeton. 2008.