***This event is in-person and open only to Princeton University ID holders**

## Graph limits and graph homomorphism inequalities

**Abstract**: Graph limits is a recently developed 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? For example, we show this perspective recently helps us answer a question on Ramsey theory raised by Jagger-Stovicek-Thomason’96, Hatami-Hladky-Kral’-Norine-Razborov’12, Conlon-Fox-Sudakov’15, where they asked whether there are common graphs with arbitrarily large chromatic numbers. This is based on a joint work with Dan Kral' and Jan Volec.

**Bio**:** **Fan Wei is a mathematician working in extremal and probabilistic combinatorics with applications to theoretical computer science. She completed her PhD at Stanford University in 2019 under the supervision of Jacob Fox. After spending a year at IAS, she is now an instructor in the Department of Mathematics at Princeton University

_{.}Her work was funded under Simons Foundation, Algorithms & Geometry Unit in 2020, and is currently funded under NSF Award DMS-1953958.