My primary research is in homotopy theory. In particular, I'm thinking about the relationship between operads and symmetric monoidal categories. You can watch an introductory talk on some of my work here.
I am also working on two collaborative projects. In the first collaboration, we study principal 2-group bundles. In particular, we have given an explicit description of the bicategory of flat 2-group bundles on an oriented surface. This project is with Daniel Berwick-Evans, Emily Cliff, Laura Murray, and Apurva Nakade.
The second collaboration studies the applications of weakly globular double categories, a simplicial model of bicategories that is a sub-2-category of the 2-category of double categories. Here is a video about weakly globular double categories and the very beginning steps of our work. This project is mentored by Simona Paoli, and also includes Elise McMahon, Claire Ott, Daniel Plácido, and Maru Sarazola.
An overview of all of my research projects as of October 2021
The moduli of 2-group bundles, flat string structures, and a categorification of the Freed-Quinn line bundle, joint with D. Berwick-Evans, E. Cliff, L. Murray, A. Nakade. Available on the arXiv: 2110.07571, Submitted.
Weakly globular double categories: a model for bicategories, joint with Claire Ott, n-Category Café blog post.
Operads and localizations: a comparison, University of Virginia Topology Seminar, University of Virginia, online. February 2022.
An algebraic description of principal 2-group bundles, Johns Hopkins Topology Seminar, Johns Hopkins University, online. January 2022.
Principal 2-group bundles, Southampton Topology Seminar, University of Southampton, online. December 2021.
An introduction to applied category theory, Providence College Department Colloquium, online. November 2021.
Principal 2-group bundles. GROOT Summer Seminar, online. August 2021. (video)
Weakly globular double categories and Petri nets, with E. McMahon, C. Ott. Applied Category Theory, online. July 2021. (video)
Hammocks and Trees: A Comparison of Localizations of Operads. Young Topologists Meeting, online. July 2021. (video)
A Double Categorical Model of Weak 2-categories, with C. Ott. The Adjoint School, online. June 2021.
Localizations of Operads. Topology in Distinct Flavours, online. June 2021.
What is an Operad?. UNH Mathematics Graduate Seminar, online. November 2020.
Operads and Localizations. Women in Mathematics in New England, online. October 2020.
Counting Votes. UNH Mathematics Graduate Seminar Gong Show, online. October 2020.
Desmos Classroom Activities. UNH Mathematics Graduate Seminar, Durham, NH. December 2019.
Homotopy Theories and Model Categories. eCHT Kan Seminar, online. October 2019.
Geogebra and Calculus. UNH Mathematics Graduate Seminar, Durham, NH. September 2019.
Categories and ∞-categories. UNH Graduate Research Conference, Durham, NH. April 2019.
An Intoduction to Categories. UNH Mathematics Graduate Seminar, Durham, NH. September 2018.
Adjunctions, Limits, and Colimits in Homotopy 2-categories. MIT Talbot Workshop 2018: Model Independent Theory of ∞-categories, Government Camp, OR. May 2018.
The Adjoint School, Spring 2021.
AMS Mathematics Research Community: Geometric Representation Theory and Equivariant Elliptic Cohomology, June 2019.
eCHT Kan Seminar, Fall 2019.
MIT Talbot Workshop: Model Independent Theory of ∞-categories, May 2018.