Winterschool

Jan 28—Feb 4, 2017

The Winter School in Abstract Analysis (section Set Theory) is a traditional conference for mathematicians working in diverse areas of Set Theory, Topology and Analysis. The school is a meeting where emphasis is put on the joy of doing mathematics. The invited speakers for this year are

D. Asperó, J. Bagaria, Ch. Brech, A. Marks.

More information can be found at winterschool.eu/2017.

Research Interests

My main area of interest is Set Theory, in particular combinatorics of $\omega$. Anything having to do with (ultra)filters will certainly pique my interest. Some of my recent work centers around definable ideals on $\omega$ and (generalized) Mathias forcing. I also occasionaly dabble with general and set-theoretic topology. I didn't (yet?) do any research in computer science, but it definitely is an interesting area.

Publications

2019

• M. Habič, J. Hamkins, L. Klausner, J. Verner, K. Williams: Set-theoretic blockchains, Archive for Mathematical Logic, vol. 58, no. 7-8, pp. 965–997 (2019) (url, doi:10.1007/s00153-019-00672-z)
• D. Raghavan, J. Verner: Chains of P-points, Canadian Mathematical Bulletin, vol. 62, no. 4, pp. 856–868 (2019) (, doi:10.4153/S0008439519000043)
• 2018

• T. Lavicka, J. Verner: Completely separably MAD families and the modal logic of $\beta\omega$, Journal of Symbolic Logic, (2018) (, arxiv:1709.06862)
• S. Shelah, J. Verner: Ramsey partitions of metric spaces, None, (2018) ()
• J. Brendle, B. Farkas, J. Verner: Towers in Filters, Cardinal Invariants and Luzin Type Families, Journal of Symbolic Logic, vol. 83, no. 3, (2018) (, doi:10.1017/JSL.2017.52)
• 2016

• R. Honzík, J. Verner: A lifting argument for generalized Gregorieff forcing, Notre Dame Journal of Formal Logic, vol. 2016, no. 57 (2), (2016) (, doi:10.1215/00294527-3459833)
• D. Chodounský, J. Verner: Toposym Book of Abstracts (other)
• W. Brian, J. Verner: $G_\delta$ and co-meager semifilters, Fundamenta Mathematicae, vol. 2016, no. 235, (2016) (, arxiv:1503.06092, doi:10.4064/fm182-2-2016)
• 2013

• J. Verner: Filter convergence in $\beta\omega$, Acta Universitatis Carolinae. Philosophica et Historica, vol. 2010, no. 2, (2013) (url)
• J. Verner: Lonely points revisited, Commentationes Mathematicae Universitatis Carolinae, vol. 54, no. 1, (2013) (url)
• A. Blass, M. Hrušák, J. Verner: On strong $P$-points, Proceedings of the American Mathematical Society, vol. 141, (2013) (, doi:10.1090/S0002-9939-2013-11518-2)
• 2011

• M. Hrušák, J. Verner: Adding ultrafilters by definable quotients, Rendiconti del Circolo Matematico di Palermo, vol. 60, no. 3, (2011) (, doi:10.1007/s12215-011-0064-0)
• T. Pazák, J. Verner: Toposym 2011 Book of Abstracts (other)
• 2008

• J. Verner: Lonely points in ω*, Topology and its Applications, vol. 155, (2008) (, doi:10.1016/j.topol.2008.05.020)

Miscellanea

• Semiselective coideals (picture), derived from a talk by E. Thuemmel at the Prague Set Theory seminar
• ZFC inequalities between Cardinal invariants of the continuum (jpg, pdf), a fusion of Cichon's diagram with the Hasse diagram from Blass's Handbook article which can be found here.