Thomas Gilton

General

Welcome! I am a visiting assistant professor in the department of mathematics at the University of Pittsburgh.

My research is in Set Theory, a branch of mathematics devoted to studying the infinite. More specifically, I work in combinatorial set theory, focusing on obtaining consistency results (usually from Large Cardinals) with the standard axiom system, ZFC, for Mathematics. So far, I have focused on questions relating to obtaining models with a "large continuum", generalizations of Ramsey's Theorem to uncountable infinities (more specifically, so-called Open Coloring Axioms), and other compactness and incompactness phenomena in set theory, such as stationary reflection, and various properties of trees. I am also interested in set-theoretic topology.

In 2019 I received my Ph.D. under the supervision of Itay Neeman from the Department of Mathematics at the University of California, Los Angeles.

Papers (in reverse chronological order)

• Trees and Stationary Reflection at Double Successors of Regular Cardinals (with Maxwell Levine and Šárka Stejskalová)
  Accepted for Publication, Journal of Symbolic Logic
  pdf

• Club Stationary Reflection and the Special Aronszajn Tree Property (with Omer Ben-Neria)
  Accepted for Publication, Canadian Journal of Mathematics (The current draft has minor errors which will be corrected)
  pdf

• Abraham-Rubin-Shelah Open Colorings and a Large Continuum (with Itay Neeman)
  Accepted for Publication in the Journal of Mathematical Logic
  pdf

• A Note on the Eightfold Way (with John Krueger)
  Proceedings of the American Mathematical Society 148 (2020), no. 3, 1283-1293
  pdf

• The Harrington-Shelah Model with Large Continuum (with John Krueger)
  Journal of Symbolic Logic, 84 (2019), no. 2, 684-703
  pdf

• Side Conditions and Iteration Theorems (with Itay Neeman)
  From the April 9th, 2016 AST conference
  pdf

• Mitchell's Theorem Revisited (with John Krueger)
  Annals of Pure and Applied Logic, Volume 168 (2017), no. 5, pp 922-1016
  pdf

Selected Talks

• Club Stationary Reflection and the Special Aronszajn Tree Property
  BLAST 2021 Conference and the 2021 Boise Extravaganza in Set Theory (aka 2021 B.E.S.T.)
  Click here for slides.

• ARS Open Colorings and a Large Continuum
  Fields Institute, Set Theory Seminar. December 04, 2020.
  Click here for slides (I corrected some typos on 07/07/21).

Notes and Other Writing

• You can find a copy of my Ph.D. thesis here.
• My CV is available here

Current Teaching

Personal