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.
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. |
KleisliCategories.v, part of the UniMath Library. [Git] |
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].
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. |
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. |
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. |
x@fsu.edu, for x = bdoherty