Omer Mermelstein : On flat combinatorial pregeometries and hypergraphs.

Posted by James Freitag , part of the Logic Seminar.

At

Oct. 2, 2018, 3:30 p.m.

In

427 SEO

Abstract

The property of "flatness" of a pregeometry (matroid) is best known in model theory as the device with which Hrushovski showed that his example refuting Zilber's conjecture does not interpret an infinite group. Indeed, the pregeometry associated to any hypergraph via Hrushovski's delta-function is flat, and it is known that any finite flat pregeometry (strict gammoid) can be gotten froma hypergraph. In this talk, we will explain what flatness actually is, show that the interplay between hypergraphs and flat pregeometries runs deeper than the finite case, present some limited results and conjectures based on these.