Dr Łukasz Grabowski

Lecturer in Pure Mathematics

Research Overview

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.

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.
Journal article

Measurable circle squaring
Grabowski, Ł., Máthé, A., Pikhurko, O. 1/03/2017 In: Annals of Mathematics. 185, 2, p. 671-710. 40 p.
Journal article

Irrational l2 invariants arising from the lamplighter group
Grabowski, Ł. 2016 In: Groups, Geometry, and Dynamics. 10, 2, p. 795-817. 23 p.
Journal article

Groups with Identical k-Profiles
Glauberman, G., Grabowski, Ł. 23/12/2015 In: Theory of Computing. 11, p. 395-401. 7 p.
Journal article

Group ring elements with large spectral density
Grabowski, Ł. 1/10/2015 In: Mathematische Annalen. 363, 1, p. 637-656. 20 p.
Journal article

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.
Journal article

On Turing dynamical systems and the Atiyah problem
Grabowski, Ł. 1/10/2014 In: Inventiones Mathematicae. 198, 1, p. 27-69. 43 p.
Journal article