Garrett Ervin

Harry Bateman Postdoctoral Scholar
Division of Physics, Mathematics and Astronomy
California Institute of Technology
Kellogg Laboratory 204
gervin [at] caltech [dot] edu

About

I am a postdoc in mathematics at Caltech. My research interests are in set theory, order theory, and combinatorics. Much of my work concerns the structural arithmetic of linear orders. My postdoc adviser at Caltech is Alekos Kechris; I was previously a postdoc in the math department at Carnegie Mellon under Clinton Conley. Before that, I was at UC Irvine, doing my Ph.D. under Martin Zeman. You can find my CV here.

During the spring quarter of 2025, I am teaching Ma / CS 6c: Introduction to Mathematical Logic. In the past, I've taught upper division courses in logic, set theory, model theory, and computability theory, and introductory courses on proofs and proof writing, linear algebra, and calculus. I authored the complete course content for a course on set theory and forcing in the spring of 2024 (at Caltech), as well as a topics course Linear Orders in the fall of 2022 (at Caltech), and a new course Linear Algebra for Data Science in the fall of 2021 (at CMU).

Papers and preprints

  1. Every linear order isomorphic to its cube is isomorphic to its square (Advances in Mathematics 313 (2017): 237-281)
  2. Distinct orders dividing each other on both sides (Proceedings of the AMS 147 (2019): 3729-3741)
  3. Decomposing the real line into everywhere isomorphic suborders (Proceedings of the AMS: 152.03 (2024): 925-939)
  4. (with Ethan Gu) Left absorption in products of countable orders (Order (Dec. 17, 2024): 1-25)
  5. Self-embeddings of linear orders (preprint)
  6. Maximum flows in networks of {0,1}-valued infinitary submodular functions (preprint)
  7. (with Eric Paul) The additive arithmetic of linear orders (preprint)

Works in progress and rough drafts

  1. (with Eric Paul) Cancellation and absorption in products of linear orders

Linear orders sketchbook

My thesis

Selected Slides

  1. A dichotomy theorem for order types of orbit equivalence relations on R
  2. Arithmetic of linear orders
  3. Infinitary submodular functions and filter flows
  4. Filter flows
  5. Self-similar structures
  6. The cube problem for linear orders

Current Teaching (at Caltech)

  1. Intro to Logic, Spring, 2025

Past Teaching (at Caltech)

  1. Computability Theory II, Winter, 2025
  2. Computability Theory I, Fall, 2024
  3. Set Theory II Spring, 2024
  4. Set Theory I Winter, 2024
  5. Model Theory Fall, 2023
  6. Computability Theory III Spring, 2023
  7. Computability Theory II Winter, 2023
  8. Linear Orders Fall, 2022

Past Teaching (at CMU)

  1. Concepts of Mathematics Spring, 2022
  2. Linear Algebra For Data Science Fall, 2021
  3. Concepts of Mathematics Spring, 2021
  4. Integration and Approximation Fall, 2020
  5. Concepts of Mathematics Summer II, 2020
  6. Concepts of Mathematics Spring, 2020
  7. Integration and Approximation Fall, 2019
  8. Concepts of Mathematics Spring, 2019
  9. Basic Logic Fall, 2018
  10. Concepts of Mathematics Summer II, 2018