Finite Hypergraph Families with Rich Extremal Turan Constructions via Mixing Patterns

Abstract

Previously, it was shown by the speaker that for any-graph patternthere is a finite forbidden familysuch that maximum recursive blow-ups ofare precisely maximum-free-graphs. I will discuss joint work with Xizhi Liu where we extend this result by allowing to mix different patterns and present some applications to finding finite forbidden families with rich sets ofextremal Turan constructions.

Speaker Intro

Oleg Pikhurko received his undergraduate degree from L'viv State University, Ukraine, in 1995 and his PhD from the University of Cambridge, UK, in 2000. He had a Junior Research Fellowship at St John's College, Cambridgeand a faculty position at Carnegie Mellon University. He is a professor at the University of Warwick, working there since 2011. He held an ERC Starting Grant 2012-8 and is currently supported by a Leverhulme Research Project Grantand an ERC Advanced Grant. His research interests include extremal and probabilistic combinatorics, descriptive combinatorics and limits of discrete structures.