RESEARCH
Tutorial on projective Fraïssé theory from the Winter School 2023 in Štěkeň:
Publications and preprints:
Projective Fraïssé limits of trees with confluent epimorphisms (with W. Charatonik, R. Roe and S. Yang), submitted, arXiv:2312.16915
The projective Fraisse limit of the class of all connected finite graphs with confluent epimorphisms (with W. Charatonik and R. Roe), submitted, arXiv:2206.12400
Projective Fraïssé limits and generalized Ważewski dendrites (with A. Codenotti), accepted to Fundamenta Mathematicae, arXiv:2210.06899
The automorphism group of the random poset does not admit a generic pair (with Aristotelis Panagiotopoulos), preprint, arXiv:2012.04376
Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures (with Filippo Calderoni and Katrin Tent), J. Algebra 580 (2021), 43-62. arXiv:1908.05249
Ordered structures and large conjugacy classes (with Maciej Malicki), Journal of Algebra, Volume 557, 1 September 2020, Pages 67-96. arXiv:1903.00936
Universal minimal flows of generalized Ważewski dendrites, the Journal of Symbolic Logic, Volume 83, Issue 4, December 2018, pp. 1618-1632. arXiv:1711.0786
Topologically 2-generated groups (with Maciej Malicki), pdf
Automorphism groups of countable structures and groups of measurable functions (with Maciej Malicki), Israel Journal of Mathematics, Volume 230, Issue 1, March 2019, pp 335-360. arXiv:1612.03106
The universal minimal flow of the homeomorphism group of the Lelek fan (with Dana Bartošová), Trans. Amer. Math. Soc. 371 (2019), 6995-7027. arXiv:1706.09154
Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan (with Dana Bartošová), Journal of Combinatorial Theory, Series A, Volume 150, August 2017, Pages 108-136. arXiv:1411.5134
The Lelek fan and the Poulsen simplex as Fraïssé limits (with Wiesław Kubiś), RACSAM, October 2017, Volume 111, Issue 4, pp 967-981. arXiv:1512.09252
A classification of orbits admitting a unique invariant measure (with Nathanael Ackerman, Cameron Freer, and Rehana Patel), Annals of Pure and Applied Logic, 168, no. 1, 19-36, 2017. arXiv:1412.2735
Lelek fan from a projective Fraïssé limit (with Dana Bartošová), Fundamenta Mathematicae 231 (2015), 57–79. arXiv:1411.5134
Large conjugacy classes, projective Fraïssé limits, and the pseudo-arc, Israel Journal of Mathematics, 2014, Volume 201, Issue 1, pp 75-97. PDF
The group of homeomorphisms of the Cantor set has ample generics, Bulletin of the London Mathematical Society, (2012) 44 (6): 1132-1146. PDF Comment: In Theorem 4.1, in the assumptions, the following condition is missing:
(3) Let R be one of s_1, s_1^{-1}, s_2, s_2^{-1},..., s_m, s_m^{-1}. If x is not R^A-outgoing, then there exists exactly one y such that R^A(x,y). Thanks to Shujie Yang for pointing that out.
Spatial models of Boolean actions and groups of isometries (with Sławomir Solecki), Ergodic Theory Dynam. Systems 31 (2011), 405-421. PDF
An introduction to hyperlinear and sofic groups
(with Vladimir Pestov), Appalachian Set Theory, London Mathematical Society Lecture Notes Series, to appear. arXiv:0911.4266v2
These are lecture notes from the Appalachian Set Theory Workshop led by V. Pestov.
Continuous functions taking every value a given number of times, Acta Math. Hungar. 121 (2008), no. 3, 229-242. PDF