Projects in Mathematics Muenster

Research area A: Arithmetic and Groups
Unit A2: Groups, model theory and sets

Further Projects
CRC 1442: Geometry: Deformation and Rigidity - C05: Rigidity of group topologies and universal minimal flows We will study automatic continuity and universal minimal flows for topological groups acting on geometric objects. First, we focus on rigidity of group topologies, motivated by a question due to Rosendal on the existence of a locally compact infinite group with the automatic continuity property. We want to study this question for Burger–Mozes groups. Furthermore, motivated by a question of Evans–Hubička–Nešetřil, we want to understand when universal minimal flows of kaleidoscopic groups are metrisable. Our methods will involve interactions between group theory, topological dynamics and Ramsey theory. online

Selected Publications

Selected Publications of Aleksandra Kwiatkowska

$\bullet$ A. Kwiatkowska and M. Malicki. Automorphism groups of countable structures and groups of measurable functions. Israel J. Math., 230(1):335–360, 2019.

$\bullet$ F. Calderoni, A. Kwiatkowska, and K. Tent. Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures, arXiv eprints: 1908.05249, 2019.

$\bullet$ D. Bartošová and A. Kwiatkowska. The universal minimal flow of the homeomorphism group of the Lelek fan. Trans. Amer. Math. Soc., 371(10):6995–7027, 2019.

$\bullet$ A. Kwiatkowska. Universal minimal flows of generalized Ważewski dendrites. J. Symb. Log., 83(4):1618–1632, 2018.

$\bullet$ W. Kubiś and A. Kwiatkowska. The Lelek fan and the Poulsen simplex as Fraisse limits. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 111(4):967–981, 2017.

$\bullet$ D. Bartošová and A. Kwiatkowska. Gowers' Ramsey theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan. J. Combin. Theory Ser. A, 150:108–136, 2017.

$\bullet$ N. Ackerman, C. Freer, A. Kwiatkowska, and R. Patel. A classification of orbits admitting a unique invariant measure. Ann. Pure Appl. Logic, 168(1):19–36, 2017.

$\bullet$ D. Bartošová and A. Kwiatkowska. Lelek fan from a projective fraissé limit. Fund. Math., 231(1):57–79, 2015.

$\bullet$ A. Kwiatkowska. The group of homeomorphisms of the Cantor set has ample generics. Bull. Lond. Math. Soc., 44(6):1132–1146, 2012.

$\bullet$ A. Kwiatkowska and S. Solecki. Spatial models of Boolean actions and groups of isometries. Ergodic Theory Dynam. Systems, 31(2):405–421, 2011.

Current Publications

$\bullet $ Włodzimierz J. Charatonik, Aleksandra Kwiatkowska, and Robert P. Roe. Projective Fraïssé limits of graphs with confluent epimorphisms. arXiv e-prints, June 2022. arXiv:2206.12400.

$\bullet $ Filippo Calderoni, Aleksandra Kwiatkowska, and Katrin Tent. Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures. J. Algebra, 580:43–62, August 2021. doi:10.1016/j.jalgebra.2021.03.028.

$\bullet $ Aleksandra Kwiatkowska and Aristotelis Panagiotopoulos. The automorphism group of the random poset does not admit a generic pair. arXiv e-prints, December 2020. arXiv:2012.04376.

$\bullet $ Aleksandra Kwiatkowska and Maciej Malicki. Ordered structures and large conjugacy classes. J. Algebra, 557:67–96, September 2020. doi:10.1016/j.jalgebra.2020.03.021.

$\bullet $ Dana Bartošová and Aleksandra Kwiatkowska. The universal minimal flow of the homeomorphism group of the Lelek fan. Transactions of the American Mathematical Society, 371(10):6995–7027, May 2019. doi:10.1090/tran/7548.

$\bullet $ Aleksandra Kwiatkowska and Maciej Malicki. Automorphism groups of countable structures and groups of measurable functions. Israel Journal of Mathematics, 230(1):335–360, March 2019. doi:10.1007/s11856-018-1825-7.