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Measurable Combinatorics

This is the webpage of the Leverhulme Research Project Grant RPG-2018-424 "Measurable Combinatorics" (


This project will explore emerging deep connections between combinatorics and other fields such as analysis, descriptive set theory, ergodic theory, measured group theory, etc, with applications going both ways. One way of applying analytic techniques to finite graphs will be by means of graph limits (analytic objects of bounded complexity that capture asymptotic properties of large graphs). In the other direction, combinatorial techniques will be applied in search of "constructive'' solutions to some foundational mathematical problems, in particular building upon the recent remarkable results that one can split a 2-dimensional disk into ``definable'' pieces and re-arrange them to form a square.

Current Group Members


All papers (pre-publication versions) should be freely available from Please contact one of the authors if you have difficulty accessing them.

  1. (L.Grabowski, A.Mathe, OP) Measurable equidecompositions for group actions with an expansion property, 45pp.

Talks Given/Forthcoming

  • 11 Oct: OP, workshop "Measurable, Borel, and Topological Dynamics", CIRM
  • 6 Nov: OP, Old Codger's One-Day Combinatorics Colloquium, Reading
  • 21-23 Nov: OP, 3in1 Workshop on Graph Theory, Doslonce, Poland
  • 14 Jan: OP, Warwick Maths Society