## UW - PIMS Colloquium Series: Annie Raymond

- Date: 11/04/2022
- Time: 15:30

University of Washington

Understanding graphs locally

Graphs are ubiquitous in modern applications---including some very large graphs. This leads one to wonder, "How can we *understand* such large graphs?" One prevalent idea is to observe them locally: to count how many times certain substructures appear. If one knows something about the number of some particular substructures in a graph, what can one say about the number of other substructures or about global properties of the graph in general? Such problems are at the heart of extremal graph theory. In this talk, we will discuss successes and challenges in proving inequalities involving these substructures. We will also encounter *graph profiles*, complicated objects that allow us to understand all polynomial inequalities involving some fixed set of substructures.

**Location**: ECE 125

**Time**: 3.30pm - 4.30pm Pacific