- For my papers, see my Papers page
I’m interested in tame Abstract Elementary Classes. You can check out Wikipedia for more details, but the essence is that these are classes of structures in which types (appropriately defined as Galois types) satisfy a nice locality condition for equality. This locality condition can be seen as a weak form of compactness that is strong enough to recreated some classification theory, but weak enough to hold in many nonelementary classes.
My primary work and interest is around developing a classification theory for tame AECs. The “test question” here is Shelah’s Categoricity Conjecture, but this is more of an organizing/motivating idea than the real goal. The goal is to develop notions of forking and independence that give us similar insight and dividing lines from first-order classification theory.
Beyond this, I’m also interested in model theory and classification theory in other nonelementary settings and concrete examples and applications of this classification theory to other areas of mathematics.
Abutting these interests are first-order classification theory (and model theory) and the interaction between model theory and other areas of logic, especially set theory and category theory.
In 2014-2015, I gave several survey talks on tame AECs. An idealized version of the slides are available.
In Fall 2017, I taught a graduate topics course on tame AECs. A rough version of the course notes are available here (and I hope to polish them soon). In Spring 2017, Sebastien Vasey taught a graduate topics course on AECs and his notes (mostly disjoint after introductory material) are available here.