E-mail opie AT g DOT harvard DOT edu
Office SC 505g
I am a graduate student in the Harvard Department of Mathematics, working with Mike Hopkins. My interests are in homotopy theory, category theory, and algebraic geometry (and the intersection of these). My recent projects have focused on developing a theory of localization of types in homotopy type theory (analogous to that for spaces, see "Research" below) and understanding certain aspects of weak equivalences in the Joyal model structure on simplicial sets (ongoing).
I did my undergraduate at the University of Massachusetts Amherst, where I wrote an honors thesis in algebraic geometry with Jenia Tevelev. Before UMass, I was at Cape Cod Community College, where I was into physics and student journalism. After UMass, I did Part III at Cambridge.
Lucy Yang and I co-organize monthly women in math lunches at Harvard, which provide informal opportunities for women in the community to get to know each other. Please e-mail me if you would like to be added to our Google group!
I am an organizer for the MIT Talbot Workshop, along with Calista Bernard, Yajit Jain, and Sean Poherence. If you have questions or suggestions about Talbot, please feel free to reach out.
Localization in Homotopy Type Theory, with J. Daniel Christensen, Egbert Rijke, and Luis Scoccola. Accepted.
Effective divisors on moduli spaces of rational curves with marked points. Michigan Math. J. 65 (2016), no. 2, 251--285. My undergrad thesis; I also created a related database of spherical hypertree divisors generated using Macaulay2.
In summer 2018 I taught a tutorial on Category Theory.
In spring 2018 I taught Math 21b (Linear Algebra and Differential Equations) at Harvard.
Notes and expositions
A more expository slide talk on Homotopy Type Theory and the main results of Localization in homotopy type theory. Given at the Women in Homotopy Theory and AG conference in Berlin (March 2019).
May 27-June 2, 2018: Talbot 2018: Model-independent theory of $\infty$-categories (organizer).
May 16-20, 2018: Chromatic Homotopy Theory: Journey to the Frontier (participant).
January 2018: Joint Mathematics Meetings, special session on Homotopy Type Theory (invited participant).
November 2017: Women in Topology workshop, Berkeley, CA (participant).
Summer 2017: Mathematical Research Community (MRC) in Homotopy Type Theory. Snowbird, Utah (invited participant).
Spring 2016: Algebraic Geometry New England Series (AGNES), Brown RI (participant).
Summer 2015: AMS Summer Institue in Algebraic Geometry. Conference and graduate bootcamp (participant).
Spring 2015: University of Warwick Algebraic Geometry Seminar (invited speaker).
February 2014: Midwest Algebraic Geometry Graduate Conference, UIUC (invited speaker).
January 2014: Joint Mathematics Meetings (poster presenter, undergraduate poster session).
October 2013: Algebraic Geometry New England Series (AGNES), Stony Brook (poster presenter).
Summer 2013: Young Mathematicians’ Conference, OSU (poster presenter).
Summer 2013: UCLA Logic Summer School (participant).
My CV, last updated fall 2018.
Brirush - Own work, CC BY-SA 3.0, Link