I am a Hedrick Assistant Adjunct Professor and NSF Postdoc at UCLA. My postdoctoral mentor is Mike Hill and I am part of the topology group.

My interests are primarily in homotopy theory and its applications to problems in geometry and topology. In my PhD thesis, I focused on the construction and classification of complex topological vector bundles of rank three on complex projective five-space. I am currently thinking about other problems related to (unstable) vector bundles and how they can be studied using tools from chromatic homotopy theory.

I am also interested in homotopy-theoretical aspects of algebraic geometry, e.g. motivic homotopy theory. My projects in this area have involved analogues classical invariants (degree and Euler characteristic) in motivic homotopy theory. My interest in algebraic geometry goes back to my undergraduate thesis, where I studied extremal effective divisors on the moduli space of stable rational curves with marked points.

I have also worked on various topics related to abstract homotopy theory and its applications, including homotopy theory of graphs and homotopy type theory.

Before UCLA, I completed my PhD at Harvard, where I worked with Mike Hopkins. I did my undergraduate at the University of Massachusetts Amherst, and wrote an honors thesis with Jenia Tevelev. Prior to that, I earned an Associate's degree at Cape Cod Community College.

For four years, I was an organizer for the MIT Talbot Workshop. If you have questions or suggestions related to Talbot, you can e-mail talbotworkshop AT gmail DOT com; or, if you prefer, I am still happy to talk about Talbot.

My CV, last updated February 2023, is here.

- Rank-preserving additions for topological vector bundles, after a construction of Horrocks. Submitted.
- A classification of complex rank 3 bundles on complex projective 5-space. Submitted.
- Cofibration category of digraphs for path homology, with Daniel Carranza, Brandon Doherty, Chris Kapulkin, Maru Sarazola, and Liang Ze Wong. Submitted.
- Compactly Supported A^1-Euler characteristic and the Hochschild complex, with Niny Arcila Maya, Candace Bethea, Kirsten Wickelgren, and Inna Zhakarevich. In Topology and its Applications 316, July 2022.
- The trace of the A^1-local degree, with Thomas Brazelton, Robert Burklund, Stephen McKean, and Michael Montoro. In Homotopy, Homology, and Applications 23(1): 243--255, 2021.
- Localization in Homotopy Type Theory, with J. Daniel Christensen, Egbert Rijke, and Luis Scoccola. In Higher Structures, 1(4): 1--32, 2020.
- Effective divisors on moduli spaces of rational curves with marked points. In Michigan Math. J. 65(2): 251--285, 2016. My undergrad thesis; I also created a related database of spherical hypertree divisors generated using Macaulay2.

- I am not teaching in the 2022-2023 academic year.
- I was awarded a Liggett Instructor Award for excellence in teaching at UCLA, 2021-2022.
- In Winter 2022, I taught two sections of math 115A at UCLA.
- In Fall 2021, I taught two sections of math 115A (linear algebra/ intro to proofs) at UCLA.
- For the 2020-2021 academic year, I was Bok Center Pegagogy Fellow in mathematics.
- In summer 2019 I taught a tutorial on Knot Invariants and Categorification, with co-instructor Joshua Wang.
- In summer 2018 I taught a tutorial on Category Theory.
- In spring 2018 I taught Math 21b (Linear Algebra and Differential Equations) at Harvard.
- In fall 2017, I was a graduate course assistant for math 23a (Linear algebra and real analysis I) at Harvard.

Please fill out this form if you wish me to write you a recommendation letter.