Condensed Mathematics Seminar

Organizers: Juan Rodrigez-Camargo and John Morgan

Time: Monday's 2:30 - 4:00 pm
First Meeting: Sept. 11 at 2:30

Place: Room 622 Math

For an outline of the proposed topics click here

Lecture 1. Monday, Sept. 11

John Morgan
Title: Basic Definitions and Point Set Topology underlying condensed Sets

Abstract: Topological Background: A quick review of compact Hausdorff spaces, quotient maps, compactly generated topology, totally disconnected spaces, profinite spaces, projective limits. We discuss filters and ultrafilters, limit points of ultrafilters and the Stone-Cech compactification of a discrete space. Proof that the latter are extremely disconnected compact Hausdorff spaces and that every profinite space is a quotient of a compact extremely disconnected space.

We then define a condensed set as a sheaf on the Grothendieck site of profinite spaces and discuss some basic properties of condensed sets.