# Random graphs and graph limits

## Logic, Games, and Graphs Seminar

## Meeting Details

For more information about this meeting, contact Kristin Berrigan, Andrew Belmonte, Jan Reimann, Linda Westrick.

**Speaker:** Jan Reimann, Penn State University

**Abstract:** When does a growing sequence of graphs have a limit, and how can the limit object be described? A classic example is the countable, infinite random graph, also known as the Rado graph, which is the limit of a sequence of finite random graphs. In this talk, I will first introduce a relatively new, analytic approach to graph limits, which has become known as graphons.
I will then discuss the complexity of certain universal objects (FraissÃ© limits from logic), when viewed as graphons. In particular, I will show that if a 0-1-valued graphon is constructed in a "tame" way (via a kind of finite extension method), then the induced fiber topology (also known as the $r_W$-topology) is not compact.
This is joint work with Cameron Freer (MIT).

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 03/13/2019

**Time:** 2:30pm - 3:30pm