Hello, and welcome to my website! I am currently a Postdoctoral Fellow in the Department of Mathematics and Computer Science at Brandon University in Brandon, Manitoba, Canada working with Rory LucyshynWright. I obtained my PhD in mathematics at the University of Ottawa in October 2020 working with Pieter Hofstra and Philip Scott, and my MSc in Logic and Computation at Carnegie Mellon University in May 2015 working with Steve Awodey.
My research interests lie primarily in category theory and its applications to mathematics and computer science. My postdoctoral work has resulted in several contributions to the study of enriched algebraic structure, on the basis of which I am currently pursuing applications to topological algebra, and developing a (topologically) enriched treatment of algebraic datatypes and algebraic databases. My PhD research focused on the topic of isotropy and its applications to algebra and theoretical computer science, and showed that the notions of conjugation and inner automorphism can be fruitfully generalized from group theory to many other prominent areas of mathematics.
I am on Twitter! @JasonParkerMath
I am a person who stutters (or stammers), which means that I sometimes have pauses, blocks, and/or repetitions in my speech. Here are some facts and myths about stuttering, and (since some people are curious) here are some best practices for talking to a person who stutters. I am putting this information here to help increase the visibility and representation of mathematicians (and researchers/academics more generally) who stutter. I am always more than happy to talk about stuttering or answer any questions about it. One famous mathematician who stuttered is Alan Turing!
Last updated: May 15, 2023
Education
September 2015  October 2020
PhD in Mathematics and Statistics, University of Ottawa
Thesis: Isotropy Groups of QuasiEquational Theories
Advisors: Pieter Hofstra and Philip Scott
August 2013  May 2015
MSc in Logic, Computation, and Methodology, Carnegie Mellon University
Thesis: Duality between Cubes and Bipointed Sets
Advisor: Steve Awodey
September 2009  April 2013
BA Honours in Philosophy, Queen's University
Publications

Diagrammatic presentations of enriched monads and varieties for a subcategory of arities (with Rory LucyshynWright). Preprint, 2022. To appear in Applied Categorical Structures.

Exponentiability in categories of relational structures. Theory and Applications of Categories, Vol. 39, No. 16, 2023, 493518.

Inner automorphisms of presheaves of groups. Applied Categorical Structures 31:20, 2023. arXiv:2107.13989

Presentations and algebraic colimits of enriched monads for a subcategory of arities (with Rory LucyshynWright). Theory and Applications of Categories, Vol. 38, No. 38, 2022, 14341484.

Extensivity of categories of relational structures. Theory and Applications of Categories, Vol. 38, No. 23, 2022, 898912.

Locally bounded enriched categories (with Rory LucyshynWright). Theory and Applications of Categories, Vol. 38, No. 18, 2022, 684736.

Covariant isotropy of Grothendieck toposes and extensive categories. Applied Categorical Structures 30, 779803, 2022. arXiv:2104.13487

Polymorphic automorphisms and the Picard group (with Pieter Hofstra and Philip Scott). 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021), N. Koyayashi, Ed. Dagstuhl Publications LIPlcs, Vol. 195, 2021.

Isotropy groups of free racks and quandles. Journal of Algebra and its Applications, Vol. 21, No. 8, 2250163, 2022. arXiv:2010.09837

Isotropy of algebraic theories (with Pieter Hofstra and Philip Scott). Electronic Notes in Theoretical Computer Science 341: 201217, 2018.
Preprints

Enriched structuresemantics adjunctions and monadtheory equivalences for subcategories of arities (with Rory LucyshynWright). Preprint, 2023. arXiv:2305.07076. Submitted for publication.

Isotropy and combination problems. Preprint, 2020.
Selected Presentations
Isotropy groups of locally finitely presentable and extensive categories.

Invited Talk: Category Theory Octoberfest 2022. Online. October 29, 2022. Slides, video.
Enriched structuresemantics adjunctions and monadtheory equivalences for subcategories of arities.

Applied Category Theory International Conference. University of Strathclyde, Glasgow. July 22, 2022. Slides, video (starts at ~6:09:25).

New York City Category Theory Seminar. Online. April 6, 2022. Slides, video.

University of Ottawa Logic Seminar. Online. March 18, 2022. Slides.

Atlantic Category Theory Seminar. Online. March 8, 2022. Slides.
Locally bounded enriched categories.

Australian Category Seminar. Online. November 9, 2021. Slides.

The Calgary Peripatetic Seminar. Online. October 1, 2021. Slides.

University of Ottawa Logic Seminar. Online. September 30, 2021. Slides, video.

Atlantic Category Theory Seminar. Online. September 14, 2021. Slides.
Presentations and algebraic colimits of enriched monads (for a subcategory of arities).

Category Theory Novemberfest. Online. November 13, 2021. Slides, video.

Atlantic Category Theory Seminar. Online. October 5, 2021. Slides.

International Category Theory Conference 2021. Genoa, Italy. August 31, 2021. Slides, video.

Mathematical Congress of the Americas Categories and Topology Session. July 16, 2021. Slides, video.
Polymorphic automorphisms and the Picard group.

Invited Talk: Carnegie Mellon University Mathematical Logic Seminar. Online. October 26, 2021. Slides.

Logic Supergroup Early Career Researcher Workshop. Online. October 14, 2021. Slides, video.

6th International Conference on Formal Structures for Computation and Deduction. Buenos Aires, Argentina. July 21, 2021. Slides, video.

Distinguished Presentation: Applied Category Theory Conference. University of Cambridge. July 15, 2021. Slides, video.
Covariant isotropy of Grothendieck toposes.

Open House on Category Theory. Online. November 19, 2021. Slides.

Toposes Online Conference. Online, June 30, 2021. Slides, video.
Isotropy in category theory.

Invited Talk: Brandon University Science Seminar. Brandon University. March 25, 2021. Slides.
Isotropy groups of quasiequational theories.

Invited Talk: TalTech Category Theory Seminar. Online. March 4, 2021. Slides.

New York City Category Theory Seminar. Online, February 3, 2021. Slides, video.

Panglobal Algebra and Logic Seminar (PALS). Online, January 26, 2021. Slides, video.

AlgebraCoalgebra Seminar. Online, January 6, 2021. Slides.

The Calgary Peripatetic Seminar. Online. December 11, 2020. Slides.

Vanderbilt University Universal Algebra and Logic Seminar. Online. December 7, 2020. Slides.

Cambridge University Category Theory Seminar. Online. December 1, 2020. Slides.

Atlantic Category Theory Seminar. Online. November 3, 2020. Slides.

Australian Category Theory Seminar. Online. October 21, 2020. Slides.
Isotropy of algebraic theories.

Université catholique de Louvain Category Theory Seminar. Université catholique de Louvain. September 11, 2018. Slides.

Mathematical Foundations of Programming Semantics Conference. Dalhousie University. June 8, 2018. Slides.

Canadian Mathematical Society Summer Meeting, Graduate Student Session. University of New Brunswick. June 4, 2018. Slides.

Foundational Methods in Computer Science Conference. University of Ottawa. June 10, 2017. Slides.
Duality between cubes and bipointed sets.

Category Theory Octoberfest. University of Ottawa. October 2015.
Teaching
Brandon University:

Course Instructor for Contemporary Mathematics (62:152), Winter 2023

Course Instructor for Introduction to Statistics (62:171), Winter 2023

Course Instructor for Introduction to Statistics (62:171), Fall 2022

Course Instructor for Logic (70:240), Fall 2021

Guest Instructor for Introduction to Set Theory and Logic (62:261), October 2020
I also have 8 years of extensive experience as a teaching assistant in mathematics (and logic); please see my CV for complete details.