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.
Host: Alexander Razborov
Fan Wei is currently an instructor at Department of Mathematics, Princeton university. Prior to that, she has been at IAS and was a PhD student at Stanford University under the supervision of Jacob Fox. Fan will join Duke University as an assistant professor in mathematics in Fall 2023. Her research interests include combinatorics, graph theory, probabilistic methods, and applications in theoretical computer science.