# 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 L^{2}-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.

## Web Links

My personal webpage: http://www.lancaster.ac.uk/staff/grabows1/

LIMITS: Limits of Structures in Algebra and Combinatorics

01/02/2019 → 31/01/2024

Research

- Algebra and Geometry