**Abstract:**

Graph limits is a powerful theory in studying graphs from a continuous perspective. In this talk, we will show how the perspective of graph limits helps with graph homomorphism inequalities and how to make advances in a common theme in extremal combinatorics: when does randomness give nearly optimal bounds? In particular we show how this perspective recently helped us answer a question on Ramsey theory raised by Jagger-Stovicek-Thomason’96, Hatami-Hladky-Kral-Norine-*common* graphs with arbitrarily large chromatic numbers. This is based on a joint work with Dan Kral and Jan Volec.

**Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10. Both will be online only.**

**Join Zoom Meeting: https://washington.zoom.us/j/ 91547335974Meeting ID: 915 4733 5974**