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.

  • Algebra and Geometry