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'm currently teaching a course on the arithmetic of linear orders and one-dimensional dynamics (at ELTE). 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
- (with Eric Paul) The additive arithmetic of linear orders (preprint)
- Here is an old version of the paper, that takes a different approach.
- Eric has formalized some of our work in Lean!
- (with Alvaro Diaz Ramos and Saharon Shelah) Generalized sums of linear orders (preprint)
- (with Alberto Marcone and Thilo Weinert) Untranscendable order types (preprint)
- Maximum flows in networks of {0,1}-valued infinitary submodular functions (preprint)
- Self-embeddings of linear orders (preprint)
- (with Ethan Gu) Left absorption in products of countable orders (Order (Dec. 17, 2024): 1-25)
- Decomposing the real line into everywhere isomorphic suborders (Proceedings of the AMS: 152.03 (2024): 925-939)
- Distinct orders dividing each other on both sides (Proceedings of the AMS 147 (2019): 3729-3741)
- Every linear order isomorphic to its cube is isomorphic to its square (Advances in Mathematics 313 (2017): 237-281)
In progress
- (with Eric Paul) Cancellation and absorption in products of linear orders
