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, algebraic geometry, and the intersection of these. Recently I've been thinking about algebraic K-theory, and questions about algebraicity of vector bundles. My other grad school 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, but currently on hold).
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.
I am involved with monthly women in math lunches at Harvard, now organized by Lucy Yang and Gwyneth Moreland. These provide informal opportunities for women in the community to get to know each other. Please feel free to e-mail me if you would like to know more!
I am an organizer for the MIT Talbot Workshop, along with Calista Bernard, Yajit Jain, and Lucy Yang. If you have questions or suggestions related to Talbot, contact me or e-mail talbotworkshop AT gmail DOT com.
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.
Localization in Homotopy Type Theory, with J. Daniel Christensen, Egbert Rijke, and Luis Scoccola. To appear in Higher Structures.
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 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.
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).
Travel (planned and past)
June 21-27, 2020: MIT Talbot Workshop (organizer).
February 6-14, 2020: Connections for Women and Introductory Workshop, MSRI program on Higher categories and categorification .
January 5-10, 2020: San Diego for Homotopy Type Theory Formalization Bootcamp.
August 26-30, 2019: Women in Topology III, Bonn, Germany. Project group led by Inna Zhakarevich and Kirsten Wickelgren.
July 7-13, 2019: European Talbot: Algebraic K-Theory, Rheinboellen, Germany. Talk on Contintuity for K-theory and TC, based on Clausen--Mathew--Morrow.
May 27-31, 2019: Graduate Summer School on Hitchins Systems, Stony Brook.
April 7-13, 2019: Talbot 2019: Moduli spaces of manifolds (organizer).
March 20-22, 2019: Women in homotopy theory and algebraic geometry II, Freie Universit Berlin. (Speaker, see above for slides.)
March 2-6, 2019: Arizona Winter School on Topology and Arithmetic. Participated in Kirsten Wickelgren’s project group.
January/February 2019: Connections for Women and Introductory Workshop, MSRI semester programs on Derived Categories and on Birational Geometry of Moduli Spaces.
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 2019.
Brirush - Own work, CC BY-SA 3.0, Link