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 Lucyshyn-Wright. 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.    

Click on the link on the lefthand menu to open my CV (which contains my e-mail address). Also, check out the math memes page to nerd out like a mathematician (more to be added in the future!).

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 here are some best practices for talking to a person who stutters (or to anyone, really!). I am putting this information here to help increase the visibility and inclusivity 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: September 16, 2022

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Education

September 2015 - October 2020 

PhD in Mathematics and Statistics, University of Ottawa

Thesis: Isotropy Groups of Quasi-Equational 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

  1. Extensivity of categories of relational structuresTheory and Applications of Categories, Vol. 38, No. 23, 2022, 898-912.

  2. Locally bounded enriched categories (with Rory Lucyshyn-Wright). Theory and Applications of Categories, Vol. 38, No. 18, 2022, 684-736.

  3. Covariant isotropy of Grothendieck toposes and extensive categoriesApplied Categorical Structures 30, 779-803, 2022. arXiv:2104.13487

  4. 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. 

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

  6. Isotropy of algebraic theories (with Pieter Hofstra and Philip Scott). Electronic Notes in Theoretical Computer Science 341: 201-217, 2018.

Preprints

  1. Exponentiability in categories of relational structures. Preprint, 2022. Submitted for publication.

  2. Diagrammatic presentations of enriched monads and varieties for a subcategory of arities (with Rory Lucyshyn-Wright). Preprint, 2022. Submitted for publication.

  3. Presentations and algebraic colimits of enriched monads for a subcategory of arities (with Rory Lucyshyn-Wright). Preprint, 2022. Submitted for publication.

  4. Inner automorphisms of presheaves of groups. Preprint, 2021. Submitted for publication.

  5. Isotropy and combination problems. Preprint, 2020. 

 

Selected Presentations

Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities.

 

Locally bounded enriched categories.

 

Presentations and algebraic colimits of enriched monads (for a subcategory of arities).

 

Polymorphic automorphisms and the Picard group.

Covariant isotropy of Grothendieck toposes.

 

Isotropy in category theory.

Isotropy groups of quasi-equational theories.

Isotropy of algebraic theories.

Duality between cubes and bipointed sets.