E-mail mopie AT math DOT ucla DOT edu
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 in homotopy theory and algebraic geometry. 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 preparing this work for publication and thinking about generalizations of its contents. Please do email me if you would like a copy of my thesis or a research statement.
My other projects have involved: studying analogues classical invariants (degree, Euler characteristic) in motivic homotopy theory and developing a theory of localization in homotopy type theory (analogous to that for spaces). Additionally, I spent some time during grad school thinking about characterizations of weak equivalences in the Joyal model structure on simplicial sets (no resulting publication). As an undergraduate, I studied extremal effective divisors on the moduli space of stable rational curves with marked points.
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 July 2022, is here.
Compactly Supported A^1-Euler characteristic and the Hochschild complex. My project at Women in Topology III , with Niny Arcila Maya, Candace Bethea, Kirsten Wickelgren, and Inna Zhakarevich. To appear in Topology and its Applications, 2022.
The trace of the A^1-local degree. Results from my 2019 Arizona Winter School project group with Thomas Brazelton, Robert Burklund, Stephen McKean, and Michael Montoro. Project supervised by Kirsten Wickelgren. 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.
(The latest arXiv version is the most up-to-date.)
I was awarded a Liggett Instructor Award for excellence in teaching at UCLA, 2021-2022.
In Winter 2022, I am teaching two sections of math 115A at UCLA (linear algebra/ intro to proofs).
In Fall 2021, I taught two sections of math 115A 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.
Travel page (planned and past)
Brirush - Own work, CC BY-SA 3.0, Link