Talk will be at meeting room at the Department of Mathematics and Statistics, 4:00 pm, 12 December, 2024

Speaker: Oleg Pikhurko (University of Warwick), https://warwick.ac.uk/fac/sci/maths/people/staff/oleg_pikhurko/

Title: Turán systems

Abstract:
A Turán (s,r)-system is an r-graph G in which every set of s vertices contains at least one edge, and the Turán density t(s,r) is the asymptotically smallest edge density of such G. The question of estimating this function received a lot of attention since it was first raised by Turán in 1941. I will give an overview of this area, including some new upper bounds on t(s,r) when r tends to infinity.

Oleg Pikhurko earned his PhD from the University of Cambridge under the supervision of Andrew Thomason in 2000. After completing his doctorate, he continued his postdoctoral research at Cambridge as a Research Fellow at St. John’s College. He then held a faculty position at Carnegie Mellon University before joining the University of Warwick, where has been a full professor since 2012. His research interests include extremal and probabilistic combinatorics, descriptive combinatorics, and limits of discrete structures. His research was supported by many prestigious grants, including two ERC grants, and has kept attracting a large amount of attention in the community. For example, his work (together with Mathé and Noel) on a constructible solution to Tarski's circle-squaring problem was featured in the Quanta magazine.