# Measurable Combinatorics

This is the webpage of the Leverhulme Research Project Grant RPG-2018-424 "Measurable Combinatorics", 1 October 2019 - 30 September 2023 (warwick.ac.uk/meascomb).

## Overview

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

- Jan Grebik (1/10/2019-present)
- Oleg Pikhurko (PI)

## Papers

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

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

## Talks Given/Forthcoming

2019

- 11 Oct: OP, Workshop "Measurable, Borel, and Topological Dynamics", CIRM
- 4 Nov: OP, Workshop "Structure, Sparsity and Randomness", Radbound University, Nijmegen
- 6 Nov: OP, Old Codger's One-Day Combinatorics Colloquium, Reading
- 21 Nov: OP, 3in1 Workshop on Graph Theory, Doslonce, Poland

2020

- 14 Jan: OP, Warwick Maths Society
- 30 Jan: OP, ACO Seminar, Carnegie Mellon University
- 11 Feb: OP, seminar, Adam Mickiewicz University, Poznan
- 17 Feb: OP, Krakow Combinatorics Seminar

### Some News

- 4 Nov'19: OP was an external examiner of François Pirot's PhD thesis at Radboud University, Nijmegen, that was successfully defended. Congratulations, François!
- 1 Jan 20: OP appointed to the Editorial Board of "Random Structures and Algorithms"