General (Main) Seminar MSRI program on DDC-Measures on perfect PAC fields
Fri, 4 December, 2020
5:00pm
Organizer: V. Harizanov and A. Shlapentokh
For link contact [email protected]
Friday, December 4, 12:00-1:00 ET on Zoom
Speaker: Zoé Chatzidakis, Ecole Normale Supérieure – CNRS, France
Title: Measures on perfect PAC fields
Abstract: This is work in progress, joint with Nick Ramsey (UCLA).
A conjecture, now disproved by Chernikov, Hrushovski, Kruckman, Krupinski, Pillay and Ramsey, asked whether any group with a simple theory is definably amenable. It is well known that the counting measure on finite fields gives rise to a non-standard counting measure on pseudo-finite fields (the infinite models of the theory of finite fields). It was unknown whether other PAC fields possessed a reasonable measure, and in this talk, we will show that some of them do, although the measure we define does not have all the nice properties of a counting measure when the field is not pseudo-finite. This result can be used to show that if G is a group definable in an e-free perfect PAC field, then G is definably amenable.
We hope to extend our results to the wider class of bounded perfect PAC fields.