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   Jason Parker

Hello, and welcome to my academic website! I am currently a Postdoctoral Scholar in the Departments of Computer Science and Mathematics at the University of Calgary in Calgary, Alberta, Canada, supervised by Robin Cockett, Kristine Bauer, Carlo Maria Scandolo, and Claude Laflamme. 

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From September 2020 to August 2023 I was a Postdoctoral Fellow in the Department of Mathematics and Computer Science at Brandon University in Brandon, Manitoba, Canada, supervised by 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. My postdoctoral work has resulted in several contributions to the study of enriched algebraic structure. 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.  

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My current academic e-mail address is: jason.parker2 AT ucalgary.ca

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I am on Twitter (@JasonParkerMath) and LinkedIn.

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I am a person who stutters (or stammers), which means that I tend to stutter a bit more than the average person! 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. One famous mathematician who stuttered is Alan Turing!

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About

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

Publications

  1. Diagrammatic presentations of enriched monads and varieties for a subcategory of arities (with Rory Lucyshyn-Wright). Applied Categorical Structures 31:40, 2023. arXiv:2207.05184

  2. Exponentiability in categories of relational structures. Theory and Applications of Categories, Vol. 39, No. 16, 2023, 493-518.

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

  4. Presentations and algebraic colimits of enriched monads for a subcategory of arities (with Rory Lucyshyn-Wright). Theory and Applications of Categories, Vol. 38, No. 38, 2022, 1434-1484.

  5. Extensivity of categories of relational structures. Theory and Applications of Categories, Vol. 38, No. 23, 2022, 898-912.

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

  7. Covariant isotropy of Grothendieck toposes and extensive categories. Applied Categorical Structures 30, 779-803, 2022. arXiv:2104.13487

  8. 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. 

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

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

Preprints

  1. Strongly finitary monads and multi-sorted varieties enriched in cartesian closed concrete categories. Preprint, 2023. arXiv:2310.04587.

  2. Free algebras of topologically enriched multi-sorted equational theories. Preprint, 2023. arXiv:2308.04531. Submitted for publication and under review.

  3. Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities (with Rory Lucyshyn-Wright). Preprint, 2023. arXiv:2305.07076. Submitted for publication and under review.

  4. Isotropy and combination problems. Preprint, 2020. 

 

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Selected Presentations

Enriched algebraic theories, monads, and varieties.

 

Diagrammatic presentations of enriched monads and the axiomatics of enriched algebra (poster).

 

Initial algebras for topologically enriched multi-sorted algebraic theories.

 

Isotropy groups of locally finitely presentable and extensive categories.

 

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.

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Covariant isotropy of Grothendieck toposes.

 

Isotropy in category theory.

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Isotropy groups of quasi-equational theories.

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Isotropy of algebraic theories.

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Duality between cubes and bipointed sets.

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Selected Presentations

Teaching

University of Calgary:

  • Course Instructor for Introduction to Statistics I (STAT213), Winter 2024

  • Course Instructor for Linear Methods I (MATH211), Fall 2023

 

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

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I also have 8 years of extensive experience as a teaching assistant in mathematics (and logic); please see my CV for complete details.

Teaching
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