Brandon Doherty

I am a postdoctoral scholar in the Department of Mathematics at Florida State University, working with Ettore Aldrovandi. I completed my PhD at the University of Western Ontario, under the supervision of Chris Kapulkin.

My main areas of research are in categorical homotopy theory and higher category theory, with a focus on model categories. In particular, I am interested in modelling higher categories using cubical sets, and in comparing simplicial and cubical models of higher categories. I am also interested in the theory of path homology of directed graphs.

Publications and preprints

► Symmetry in the cubical Joyal model structure. Submitted, 2024. [arXiv]

► (w/ D. Carranza, K. Kapulkin, M. Opie, M. Sarazola, and L. Z. Wong) Cofibration category of digraphs for path homology. Algebr. Comb., 7(2):475-514, 2024. [arXiv]

► Cubical models of higher categories without connections. J. Pure Appl. Algebra, 227(9):107373, 2023. [arXiv]

► Cubical Models of Higher Categories. PhD thesis, 2021. [UWO]

► (w/ K. Kapulkin and Y. Maehara) Equivalence of cubical and simplicial approaches to (∞,n)-categories. Adv. Math., 416:108902, 2023. [arXiv]

► (w/ K. Kapulkin, Z. Lindsey, and C. Sattler) Cubical models of (∞,1)-categories. Mem. Amer. Math. Soc., 297 (2024), no. 1484, v+110 pp. [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 2, 2023	Cubical Joyal model structures: recent and ongoing developments. [slides]. 2023 Canadian Mathematical Society Winter Meeting, Montreal.
April 11, 2023	Cubical models of higher categories without connections. [recording: Youtube]. Topolgy seminar, University of Regina, online.
February 23, 2023	Cofibration category of digraphs for path homology. [slides]. Geometric analysis seminar, Bielefeld University, online.
June 11, 2022	Cubical models of higher categories without connections. Higher Categories and Categorification, part two, Mathematical Sciences Research Institute / National Autonomous University of Mexico, Cuernavaca.
December 8, 2021	Cubical models of higher categories. Stockholm-Göteborg joint type theory seminar, Stockholm University.
September 27 - October 4, 2021	Cubical models of higher categories. University of New Brunswick, Fredericton.
December 5, 2020	Cubical models of (∞,1)-categories. [slides], [recording: Vimeo]. 2020 Canadian Mathematical Society Winter Meeting, online.
December 1, 2020	Cubical models of (∞,1)-categories. Homotopy theory seminar, Florida State University, online.
November 2, 2020	Cubical models of (∞,1)-categories. Topology seminar, Johns Hopkins University, online.
October 6, 2020	Cubical models of (∞,1)-categories. Topology seminar, École polytechnique fédérale de Lausanne, online.
June 15, 2020	Cubical models of (∞,1)-categories. [slides], [recording: Youtube]. HoTTEST Conference of 2020, online.
May 20, 2020	Necklaces and cubical categories. [slides], [recording: MSRI, Youtube]. MSRI seminar on cubical sets, online.
May 13, 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 2024	Instructor for Calculus 2 (MAC 2312).
Spring 2024	Instructor for Calculus 2 (MAC 2312).
Fall 2023	Instructor for Calculus 2 (MAC 2312).
Fall 2022	Instructor for Logic II (MM7022), Stockholm University.
Fall 2020	Instructor for Calculus I (Calculus 1000), UWO.

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

2022-2023	Organized the Logic Seminar at Stockholm University.
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@fsu.edu, for x = bdoherty