Dr Łukasz GrabowskiLecturer in Pure Mathematics
If there is a countable group somewhere in it, then I am probably interested. With this in mind, let me say that I work in Group Theory and Combinatorics.
In Group Theory, I am particularly interested in what is sometimes referred to as "Measured Group Theory", i.e. when apart from a group a prominent role is played also by a measure space, a von Neuman algebra, etc. Specific topics I find attractive include L2-Invariants, Atiyah Conjecture, Sofic Groups, Measurable Equivalence Relations, etc. I am also interested in computational and algorithmic questions.
In Combinatorics, I am involved in developing analogs of classical combinatorial theorems in the context of Borel graphs. By proxy I am also interested in applications of Borel graphs, which include classical geometrical questions, such as the Tarski Circle Squaring problem.
My personal webpage: http://www.lancaster.ac.uk/staff/grabows1/
On computing homology gradients over finite fields
Grabowski, Ł., Schick, T. 05/2017 In: Mathematical Proceedings of the Cambridge Philosophical Society. 162, 3, p. 507-532. 26 p.
Measurable circle squaring
Grabowski, Ł., Máthé, A., Pikhurko, O. 1/03/2017 In: Annals of Mathematics. 185, 2, p. 671-710. 40 p.
Irrational l2 invariants arising from the lamplighter group
Grabowski, Ł. 2016 In: Groups, Geometry, and Dynamics. 10, 2, p. 795-817. 23 p.
Groups with Identical k-Profiles
Glauberman, G., Grabowski, Ł. 23/12/2015 In: Theory of Computing. 11, p. 395-401. 7 p.
Group ring elements with large spectral density
Grabowski, Ł. 1/10/2015 In: Mathematische Annalen. 363, 1, p. 637-656. 20 p.
Vanishing of l2-cohomology as a computational problem
Grabowski, Ł. 1/04/2015 In: Bulletin of the London Mathematical Society. 47, 2, p. 233-247. 15 p.
On Turing dynamical systems and the Atiyah problem
Grabowski, Ł. 1/10/2014 In: Inventiones Mathematicae. 198, 1, p. 27-69. 43 p.