Garrett Ervin
Beginning in 2026, I will be joining the Borel Combinatorics and Complexity research group as a Momentum MSCA Postdoctoral Fellow at the Institute of Mathematics at ELTE in Budapest. My research interests are in set theory, order theory, and combinatorics. Much of my work concerns the structural arithmetic of linear orders. Previously, I was a postdoc at Caltech under Alekos Kechris; before that, I was a postdoc in the math department at Carnegie Mellon under Clinton Conley. I did my doctoral work at UC Irvine under Martin Zeman. You can find my CV here.
As an instructor, 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). Here is a teaching sample from my time at CMU.
Papers and preprints
- Every linear order isomorphic to its cube is isomorphic to its square (Advances in Mathematics 313 (2017): 237-281)
- Distinct orders dividing each other on both sides (Proceedings of the AMS 147 (2019): 3729-3741)
- Decomposing the real line into everywhere isomorphic suborders (Proceedings of the AMS: 152.03 (2024): 925-939)
- (with Ethan Gu) Left absorption in products of countable orders (Order (Dec. 17, 2024): 1-25)
- Self-embeddings of linear orders (preprint)
- Maximum flows in networks of {0,1}-valued infinitary submodular functions (preprint)
- (with Eric Paul) The additive arithmetic of linear orders (preprint)
- (with Alberto Marcone and Thilo Weinert) Untranscendable order types (preprint)
In progress
- (with Eric Paul) Cancellation and absorption in products of linear orders