Publications and submitted preprints

• [New] Quasi-invariant measures concentrating on countable structures. [Arxiv],
  Submitted July 2024. Joint work with C. Clinton and C. Jahel.
  
  
• [New] The class and dynamics of α-balanced Polish groups. [Arxiv],
  Submitted June 2024. Joint work with S. Allison.
  
  
• [New] The homeos of the Sierpinski carpet are not classifiable by countable structures. [Arxiv], Submitted April 2024. Joint work with D. Kulshreshtha.
  
  
• The definable content of homological invariants II:
  Čech cohomology and homotopy classification. [Arxiv]
  Forum of Mathematics, Pi (to appear)
  Joint work with J. Bergfalk and M. Lupini.
  
  
• The definable content of homological invariants I: Ext and lim ¹. [Arxiv]
  Proceedings of the London Mathematical Society (to appear)
  Joint work with J. Bergfalk and M. Lupini.
  
  
• Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension. [Arxiv]
  Annals of Pure and Applied Logic, 75 (5), (2024), 103412
  Joint work with A. Shani.
  
  
• Incompleteness Theorems for Observables in General Relativity. [Arxiv]
  Physical Review Letters, 131 (17), (2023), 171402
  Joint work with G. Sparling and M. Christodoulou.
  
  
• Every CBER is smooth below the Carlson-Simpson generic partition. [Arxiv]
  Fundamenta Mathematicae, 262 (1), (2023), 85-103
  Joint work with A. Wang.
  
  
• Universality vs Genericity and C₄-free graphs. [Arxiv]
  European Journal of Combinatorics, 106, (2022).
  Joint work with K. Tent.
  
  
• Examples of weak amalgamation classes. [Arxiv]
  Mathematical Logic Quarterly, 682, (2022), 178-188.
  Joint work with A. Krawczyk, A. Kruckman, and W. Kubiś.
  
  
• On Polish groups admitting non-essentially countable actions. [Arxiv]
  Ergodic Theory and Dynamical Systems, 42 (1), (2022), 180-194.
  Joint work with A.S. Kechris, M. Malicki, and J. Zielinski.
  
  
• A combinatorial model for the Menger curve. [Arxiv]
  Journal of Topology and Analysis, 14(01), (2022) 203-229.
  Joint work with S. Solecki.
  
  
• Dynamical obstructions to classification by (co)homology and other TSI-group invariants. [Arxiv]
  Transactions of the American Mathematical Society, 374(12), (2021),8793-8811.
  Joint work with S. Allison.
  
  
• Higher dimensional obstructions for star reductions. [Arxiv]
  Fundamenta Mathematicae, 255(2), (2021), 209-230.
  Joint work with A. Kruckman.
  
  
• Games orbits play and obstructions to Borel reducibility. [Arxiv]
  Groups, Geometry, and Dynamics. 12(4), (2018), 1461-1483.
  Joint work with M. Lupini.
  
  
• Extendability of automorphisms of generic substructures. [Arxiv]
  Israel Journal of Mathematics 208, (2015), 483-508.

In preparation

• The dynamics of ɑ-unbalanced Polish groups, (2024+), joint work with S. Allison.

Other Preprints and Research Notes

• The automorphism group of the random poset does not admit a generic pair.
  Preprint, December 2020. (with A. Kwiatkowska).
  Work under progress: at the moment there is a gap in the proof of Theorem 2.
• The generic combinatorial simplex. (with S. Solecki).
  Preprint, January 2020. Notes.
• Definable (co)homology, pro-torus rigidity, and (co)homological classification.
  Preprint, September 2019. (with J. Bergfalk and M. Lupini). Notes.
• Compact spaces as quotients of projective Fraisse limits.
  Preprint, January 2016. Notes.