# 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.

# 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

## 2016

• R. Honzík, J. Verner: A lifting argument for the generalized Grigorieff forcing, Notre Dame J. Formal Logic., vol. 57, no. 2, pp. 221–231 (2016) (preprint, doi:10.1215/00294527-3459833)
• W. Brian, J. Verner: $G_\delta$ semifilters and $\omega^*$, Fundamenta Mathematicae, vol. 235, pp. 153-166 (2016) (preprint, doi:10.4064/fm182-2-2016)
• ## 2015

• J. Brendle, B. Farkas, J. Verner: Towers in Filters, Cardinal Invariants and Luzin Type Families (submitted) (preprint)
• B. Farkas, J. Verner: Canonical Semifilters of Measure and Category, the Meager-Topology and Equivalence Relations (unpublished)
• ## 2013

• A. Blass, M. Hrušák, J. Verner: On strong $P$-points, Proc. Amer. Math. Soc., vol. 141, no. 8, pp. 2875–2883 (2013) (preprint, doi:10.1090/S0002-9939-2013-11518-2)
• J. Verner: Lonely points revisited, Commentationes Mathematicae Universitatis Carolinae, vol. 54, no. 1, pp. 105–110 (2013) (preprint)
• J. Verner: Filter convergence in $\beta\omega$, AUC Philosophica et Historica, Miscellanea Logica IX, vol. 2, (2013) (preprint)
• ## 2011

• J. Verner: Ultrafilters and independent systems (phdthesis)
• M. Hrušák, J. Verner: Adding ultrafilters by definable quotients, Rend. Circ. Mat. Palermo (2), vol. 60, no. 3, pp. 445–454 (2011) (preprint, doi:10.1007/s12215-011-0064-0)
• ## 2008

• J. Verner: Lonely points in $\omega^*$, Topology Appl., vol. 155, no. 16, pp. 1766–1771 (2008) (preprint, 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.