Brandon Doherty

Brandon Doherty I am a Math PhD student at the University of Western Ontario working under the supervision of Chris Kapulkin.

My main areas of research are in categorical homotopy theory and higher category theory. My most recently completed project was the construction of a model structure on the category of cubical sets which models the theory of (∞,1)-categories. I am currently working on other projects applying cubical sets to higher category theory. In the past, I have also worked on formalization of category theory in the UniMath library.

Publications and preprints

► (w/ K. Kapulkin, Z. Lindsey, and C. Sattler) Cubical models of (∞,1)-categories. Submitted. [arXiv]

► (w/ C.Ingalls and E. Faber) Computing global dimension of endomorphism rings via ladders. J. Algebra, 458:307--350, 2016. [arXiv]

Selected talks (past and scheduled)

December 5th, 2020 Cubical models of (∞,1)-categories. [slides], [recording: Vimeo]. Canadian Mathematical Society Winter Meeting, online.
December 1st, 2020 Cubical models of (∞,1)-categories. Homotopy theory seminar, Florida State University, online.
November 2nd, 2020 Cubical models of (∞,1)-categories. Topology seminar, Johns Hopkins University, online.
October 6th, 2020 Cubical models of (∞,1)-categories. Topology seminar, École polytechnique fédérale de Lausanne, online.
June 15th, 2020 Cubical models of (∞,1)-categories. [slides], [recording: Youtube]. HoTTEST Conference of 2020, online.
May 20th, 2020 Necklaces and cubical categories. [slides], [recording: MSRI, Youtube]. MSRI seminar on cubical sets, online.
May 13th, 2020 Cubical models of (∞,1)-categories. [slides], [recording: MSRI, Youtube]. MSRI seminar on cubical sets, online.

Code

KleisliCategories.v, part of the UniMath Library. [Git]

Other writings

Expository notes on ∞-cosmoi, written for a course on higher category theory. [PDF].

Computing Global Dimensions of Endomorphism Rings of Modules Over Rings of Finite Cohen-Macaulay Type, my undergraduate thesis. [PDF].

Recent teaching

Fall 2020 Instructor for Calculus I (Calculus 1000).
Fall 2019 TA for Introduction to Abstract Algebra (Math 3020) and Calculus I for the Mathematical Sciences (Calculus 1500).
Winter 2019 TA for Introduction to Cryptography (Math 3159), Intermediate Linear Algebra (Math 2120), and Methods of Matrix Algebra (Math 1229).

Scholarships and awards

2020 NSERC Michael Smith Foreign Study Supplement to participate in the program Higher Categories and Categorification at the Mathematical Sciences Research Institute in Berkeley, California. (Trip canceled due to COVID-19 pandemic.)
2018-2021 NSERC Canada Graduate Scholarship - Doctoral at UWO.
2017-2018 Ontario Graduate Scholarship at UWO.
2016-2017 NSERC Canada Graduate Scholarship - Master's at the University of Waterloo.

Service

2020 Mentored a Directed Reading Project for an undergraduate student at UWO, on Category Theory.
2019 Co-organized the math graduate seminar at UWO.

Contact information

x@uwo.ca, for x = bdoher