Aris Papadopoulos (University of Leeds)

Introduction to Graphons

Graphons ("graph"+"functions") are a fairly new piece of technology from combinatorics (they were introduced and developed by C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, B. Szegedy, and K. Vesztergombi about 15 years ago). The motivation behind graphons is to construct a space of objects which capture the concept of a "limit of a (convergent) sequence of graphs", in the same way that real numbers capture the concept of a limit of a (Cauchy) sequence of rationals. The aim of this (not exactly model theory) talk is to introduce some of the main terminology used in this area, construct the space of graphons and discuss some of the foundational theorems about this space. This talk essentially serves as an introduction to the recent preprint "Graphons arising from graphs definable over finite fields" by Džamonja and Tomašić.

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