Morgan Opie

E-mail   mopie AT math DOT ucla DOT edu
Office   MS6903
Pronouns   She/her

I am a Hendrick 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 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 homotopy theory.

I am also interested in homotopical 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 completed my undergraduate studies at the University of Massachusetts Amherst, where I wrote an honors thesis in algebraic geometry with Jenia Tevelev. I began my undergraduate degree at Cape Cod Community College.

For four years, I was an organizer for the MIT Talbot Workshop. I am still happy to talk about Talbot, but queries related to upcoming Talbots should be directed to talbotworkshop AT gmail DOT com.

My CV, last updated November 2023, is here.

Research
  • Rank-preserving additions for topological vector bundles, after a construction of Horrocks. To appear in Algebraic and Geometric Topology.
  • A classification of complex rank 3 bundles on complex projective 5-space. Submitted. This is an improvement of my main thesis results. Here is a recording of me talking about this paper.
  • Cofibration catgory of digraphs for path homology, with Daniel Carranza, Brandon Doherty, Chris Kapulkin, Maru Saruzola, and Liang Ze Wong. To appear in Algebraic Combinatorics.
  • Compactly Supported $\mathbb{A}^1$-Euler characteristic and the Hochschild complex. My project at Women in Topology III , with Niny Arcila Maya, Candace Bethea, Kirsten Wickelgren, and Inna Zhakarevich. In Topology and its Applications .
  • The trace of the $\mathbb{A}^1$-local degree, with Thomas Brazelton, Robert Burklund, Stephen McKean, and Michael Montoro. In Homotopy, Homology, and Applications.
  • Localization in Homotopy Type Theory, with J. Daniel Christensen, Egbert Rijke, and Luis Scoccola. In Higher Structures.
  • Effective divisors on moduli spaces of rational curves with marked points. In Michigan Mathematical Journal. My undergrad thesis; I also created a related database of spherical hypertree divisors generated using Macaulay2.

  • Teaching
  • In Fall 2023, I will be teaching Math 115A (linear algebra/ intro to proofs) at UCLA.
  • In Summer 2023, I led a one-week mini course on category theory as part of the UCLA's Summer Bridge Program for Cal State University.
  • In Summer 2022, I led a one-week mini course on Riemann Surfaces and algebraic geometry as part of UCLA's Summer Bridge Program for Cal State University students.
  • I was awarded a for excellence in teaching at UCLA, 2021-2022
  • In both Fall 2021 and Winter 2022, 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.

  • My travel page lists conferences I have attended or plan to attend.

    If you would like me to write you a letter of recommendation, please fill out
    this form.

    Background by Brirush - Own work, CC BY-SA 3.0, Link