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/