Jean-Simon (J-S) Pacaud Lemay Personal Webpage

I am an Associate Professor/Senior Lecturer at Macquarie University, previously I was also a DECRA Fellow.

I did my DPhil/PhD at the University of Oxford, where I was at Kellogg College and a Clarendon Scholar.

Email: js dot lemay at mq dot edu dot au

Research Areas:

Pure Mathematics
Category Theory
Differential Categories
Tangent Categories
Differential Algebras and Rota-Baxter Algebras
Foundations of Differential Geometry and Algebraic Geometry
Traced Monoidal Categories
Restriction Categories
Generalized Inverses
Theoretical Computer Science
Linear Logic
Foundations of Automatic Differentiation and Machine Learning

Reference Sites: ORCID / Google Scholar

I am always interested in new research collaborations and supervision opportunities. Feel free to contact me if you are interested in working with me or doing a PhD/masters/postdoc with me.

I am the main moderator for the category theory mailing list (categories-list@categories.org.au). To subscribe, you can email https://categories.org.au or send emails to categories-list-join@categories.org.au or categories-list-leave@categories.org.au. Also see https://ncatlab.org/nlab/show/categories+mailing+list for more info.

Academic Career (Staff Position, Postdocs, and Education):

Academic Staff Positions

Associate Professor/Senior Lecturer -- Macquarie University
Discovery Early Career Researcher Award (DECRA) Fellow -- Macquarie University

Postdoctoral Fellowships

Japan Society for the Promotion of Science (JSPS) -- Postdoctoral Fellowship -- Research Institute for Mathematical Sciences (RIMS), Kyoto University

Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Fellowship (PDF) -- Mount Allison University

Education

Doctorate in Philosophy (DPhil/PhD) in Computer Science -- University of Oxford, Kellogg College

Thesis: Revisiting Differential Categories: New Results on the Foundation of Differentiation

Supervisors: Jamie Vicary, Bob Coecke, and Luke Ong

Scholarships and Awards:

Master's of Science (M. Sc.) in Pure Mathematics -- University of Calgary

Thesis: Integral and Calculus Categories

Supervisors: Robin Cockett and Kristine Bauer

Scholarships and Awards:

Natural Sciences and Engineering Research Council of Canada (NSERC) Canada Graduate Scholarships – Master’s program
Queen Elizabeth II Graduate Scholarship
Frank & Betty Woodhams Memorial Scholarship -- Mensa Canada

Honours Bachelor of Science (B.S.) in Mathematics -- University of Ottawa

Publications:

In mathematics and theoretical computer science, authors are listed alphabetically and there is no designated lead author.

In computer science, publication in highly selective conference proceedings is regarded as more prestigious than journal publications.

For convenience, an open-source link of a pdf version is provided for each publication.

Publications (Peer-Reviewed):

JP = Journal Paper (peer-reviewed)

CP = Conference Paper published in the conference's proceedings (peer-reviewed)

[57/JP34] Free Differential Modalities (PDF)

Garner, R., & Lemay, J-S. P. (2026)

Transactions on Computational Logic.

[56/JP33] Local Categories: A New Framework for Partiality (PDF)

Lanfranchi, M. & Lemay, J-S. P. (2026)

Theoretical Computer Science.

[55/JP32] Itegories (PDF)

Cockett, R., & Lemay, J-S. P. (2026)

Mathematical Structures in Computer Science -- Special Issue dedicated to Phil Scott

[54/CP23] Generalized Inverses of Quantum Channels: a categorical perspective (PDF)

Cockett, R., Lemay, J-S. P., & Srinivasan, P. V. (2026)

Published in the proceedings of QPL2026.

[53/JP31] Derivations as Algebras (PDF)

Lemay, J-S. P. & Sava, C. (2026)

Journal Of The London Mathematical Society

[52/JP30] Cartesian Linearly Distributive Categories Revisited (PDF)

Kudzman-Blais, R., & Lemay, J-S. P. (2026)

Applied Categorical Structures

[51/JP29] Representable Tangent Structures of Affine Schemes (PDF)

Lanfranchi, M., & Lemay, J-S. P. (2026)

Theory and Applications of Categories

[50/JP28] From Abelianization to Tangent Categories (PDF)

Ikonicoff, S., Lemay, J-S. P., & Van der Linden, T. (2026)

Theory and Applications of Categories

[49/JP27] Additive Enrichment from Coderelictions (PDF)

Lemay, J-S. P. (2026)

Logical Methods in Computer Science.

[48/JP26] Properties and Characterisations of Cofree Cartesian Differential Categories (PDF)

Lemay, J-S. P. (2025)

Theory and Applications of Categories

[47/CP22] Dagger-Drazin Inverses (PDF)

Cockett, R., Lemay, J-S. P., & Srinivasan, P. V. (2025)

Published in the proceedings of QPL2025.

[46/JP25] Fundamental Theorems of Calculus and Zinbiel Algebras (PDF)

Lemay, J-S. P. (2025)

Communications in Algebra.

[45/JP24] Drazin Inverses in Categories (PDF)

Cockett, R., Lemay, J-S. P., & Srinivasan, P. V. (2025)

Theory and Applications of Categories -- Special Issue dedicated to Bill Lawvere.

[44/JP23] A Tangent Category Perspective on Connections in Algebraic Geometry (PDF)

Cruttwell, G., Lemay, J-S. P., & Vandenberg, E. (2024)

Applied Categorical Structures

[43/JP22] A Brief Survey on the Categorical Semantics for Geometry of Interaction -- In Memory of Phil Scott (PDF)

Lemay, J-S. P. (2024)

ACM SIGLOG News

[42/CP21] Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories (PDF)

Biggin, A. & Lemay, J-S. P. (2024)

Published in the proceedings of ACT2024.

[41/CP20] An Ultrametric for Cartesian Differential Categories for Taylor Series Convergence (PDF)

Lemay, J-S. P. (2024)

Published in the proceedings of MFPS2024.

[40/CP19] Laplace Distributors and Laplace Transformations for Differential Categories (PDF)

Kerjean, M. & Lemay, J-S. P. (2024)

Published in the proceedings of FSCD2024.

[39/CP18] Combining Fixpoint and Differentiation Theory (PDF)

Galal, Z. & Lemay, J-S. P. (2024)

Published in the proceedings of LICS2024.

[38/JP21] The Rosický Tangent Categories of Algebras over an Operad (PDF)

Ikonicoff, S., Lanfranchi, M., Lemay, J-S. P. (2024)

Higher Structures

[37/CP17] Reverse Tangent Categories (PDF)

Cruttwell, G., Lemay, J-S. P. (2024)

Published in the conference proceedings of CSL2024.

[36/JP20] Classical Distributive Restriction Categories (PDF)

Cockett, R. Lemay, J-S. P. (2024)

Theory and Applications of Categories -- Special Issue dedicated to Pieter Hofstra.

[35/JP19] Differential Bundles in Commutative Algebra and Algebraic Geometry (PDF)

Cruttwell, G., Lemay, J-S. P. (2023)

Theory and Applications of Categories

[34/JP18] Traced Monads and Hopf Monads (PDF)

Hasegawa, M., Lemay, J-S. P. (2023)

Compositionality.

[33/JP17] Hopf Monads on Biproducts (PDF)

Hasegawa, M., Lemay, J-S. P. (2023)

Theory and Applications of Categories.

[32/CP16] Cartesian Differential Kleisli Categories (PDF)

Lemay, J-S. P. (2023)

Published in the proceedings of MFPS2023.

[31/CP15] Graded Differential Categories and Graded Differential Linear Logic (PDF -- PDF with Appendix)

Lemay, J-S. P., Vienney, J.-B. (2023)

Published in the proceedings of MFPS2023.

[30/CP14] Moore-Penrose Dagger Categories (PDF)

Cockett, R., Lemay, J-S. P. (2023)

Published in the proceedings of QPL2023.

[29/CP13] Taylor Expansion as a Monad in Models of DiLL (PDF)

Kerjean, M., Lemay, J-S. P. (2023)

Published in the proceedings of LICS2023.

[28/JP16] Cartesian Differential Comonads and New Models of Cartesian Differential Categories (PDF)

Ikonicoff, S. & Lemay, J-S. P. (2023).

Cahiers de topologie et géométrie différentielle catégoriques.

[27/JP15] Monoidal Reverse Differential Categories (PDF)

Cruttwell, G., Gallagher, P., Lemay, J-S. P. & Pronk, D. (2023).

Mathematical Structures in Computer Science.

[26/JP14] Linearizing Combinators. (PDF)

Cockett, R., Lemay, J-S. P. (2022).

Theory and Applications of Categories.

[25/JP13] Cartesian Difference Categories. (PDF)

Alvarez-Picallo, M. & Lemay, J-S. P. (2021).

Logical Methods in Computer Science.

[24/CP12] Coderelictions for Free Exponential Modalities. (PDF)

Lemay, J-S. P. (2021).

Published in the conference proceedings of CALCO2021.

[23/CP11] Jacobians and Gradients for Cartesian Differential Categories. (PDF)

Lemay, J-S. P. (2021).

Published in the conference proceedings of ACT2021.

[22/CP10] Cartesian Difference Categories. (PDF)

Alvarez-Picallo, M., & Lemay, J-S. P. (2021).

Published in the conference proceedings of FOSSACS2020.

[21/JP12] Tensor-Restriction Categories. (PDF)

Heunen, C., Lemay, J-S. P. (2021).

Theory and Applications of Categories.

[20/JP11] Cartesian Differential Categories as Skew-Enriched Categories. (PDF)

Garner, R., Lemay, J-S. P. (2021).

Applied Categorical Structures.

[19/JP10] Integral and differential structure on the free C-infinity ring modality. (PDF)

Cruttwell, G., Lemay, J-S. P., Lucyshin-Wright R. (2021).

Cahiers de topologie et géométrie différentielle catégoriques.

[18/JP9] Differential Equations in a Tangent Category I: Complete vector fields, flows, and exponentials. (PDF)

Cockett, R., Cruttwell, G., Lemay, J-S. P. (2021).

Applied Categorical Structures.

[17/CP9] Tangent Categories from the Coalgebras of Differential Categories. (PDF)

Cockett, R., Lemay, J-S. P., & Lucyshyn-Wright, R. (2020).

Published in the conference proceedings of CSL2020.

[16/CP8] Reverse Derivative Categories. (PDF)

Cockett, R., Cruttwell, G., Gallagher, J., Lemay J-S. P., MacAdam B., Plotkin G., & Pronk, D. (2020).

Published in the conference proceedings of CSL2020.

[15/JP8] Exponential Functions for Cartesian Differential Categories. (PDF)

Lemay, J-S. P. (2020).

Applied Categorical Structures.

[14/JP7] Convenient Antiderivates for Differential Linear Categories. (PDF)

Lemay, J-S. P. (2020).

Mathematical Structures in Computer Science.

[13/JP6] Differential Categories Revisited. (PDF)

Blute, R., Cockett, R., Lemay, J-S. P., & Seely R.A.G. (2019).

Applied Categorical Structures.

[12/CP7] Why FHilb is NOT an interesting (co)differential category. (PDF)

Lemay, J-S. P. (2019).

Published in the conference proceedings of QPL2019.

[11/CP6] Higher order distributions for differential linear logic. (PDF)

Kerjean, M., & Lemay, J-S. P. (2019).

Published in the conference proceedings of FOSSACS2019.

[10/JP5] Lifting Coalgebra Modalities and MELL Model Structure to Eilenberg-Moore Categories. (PDF)

Lemay, J-S. P. (2019).

Logical Methods in Computer Science.

[9/JP4] Differential Algebras in Codifferential Categories. (PDF)

Lemay, J-S. P. (2019).

Journal of Pure and Applied Algebra.

[8/CP5] Lifting Coalgebra Modalities and MELL to EM Categories (Extended Abstract). (PDF)

Lemay, J-S. P. (2018).

Published in the conference proceedings of FSCD2018.

[7/CP4] Cartesian Integral Categories and Contextual Integral Categories. (PDF)

Cockett, R., & Lemay, J-S. P. (2018).

Published in the conference proceedings of MFPS2018.

[6/JP3] Linear Distributivity with Negation, Star-Autonomy, and Hopf Monads. (PDF)

Hasegawa, M. & Lemay, J-S. P. (2018).

Theory and Applications of Categories.

[5/JP2] A Tangent Category Alternative to the Faa di Bruno Construction. (PDF)

Lemay, J-S. P. (2018).

Theory and Applications of Categories.

[4/JP1] Integral Categories and Calculus Categories. (PDF)

Cockett, R., & Lemay, J-S. P. (2018).

Mathematical Structures in Computer Science.

[3/CP3] There is only one notion of differentiation. (PDF)

Cockett, R., & Lemay, J-S. P. (2017).

Published in the conference proceedings of FSCD2017.

[2/CP2] Integral Categories and Calculus Categories (Extended Abstract). (PDF)

Cockett, R., & Lemay, J-S. P. (2017).

Published in the conference proceedings of CSL2017.

[1/CP1] The Shuffle Quasimonad and Modules with Differentiation and Integration. (PDF)

Bagnol, M., Blute, R., Cockett, R., & Lemay, J-S. P. (2016).

Published in the conference proceedings of MFPS2016.

Preprints (Submitted to Peer-Review Journals):

[PP5] Override and Update in Restriction Categories (PDF)

Lemay, J-S. P. & Nester, C. (2025)

[PP4] From Moore-Penrose to Markov via Gauss (PDF)

Comfort, C. & Lemay, J-S. P. (2025)

[PP3] Restriction Biproducts (PDF)

Gallal, Z., & Lemay, J-S. P. (2025)

[PP2] Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories (PDF)

Di Meglio, M., Heunen, C., Lemay, J.-S. P., Perrone, P. & Stein, D. (2025)

[PP1] Important Classes of Morphisms and the Relative Cotangent Sequence in Tangent Categories (PDF)

Lemay, J-S. P. & Vooys, G. (2025)

Conference & Workshop Presentations:

[T.65] Symposium on Differentiation in category theory and program semantics

Title: A tour of the world of differential categories

[T.64] Japan Society for the Promotion of Science Alumni Association in Australia (JSPSAAA) Symposium 2025

Title: A friendly introduction to Traced Monoidal Categories with Pictures

[T.63] Australian Mathematical Society Conference (AustMS) 2025 -- Category Theory, Homotopy Theory, and K-Theory Session

Title: From Abelianization to Tangent Categories

[T.62] Australian Algebra Conference 2025

Title: Dagger-Drazin Inverses

[T.61] Category Theory Octoberfest 2025

Title: From Moore-Penrose to Markov via Gauss

[T.60] Categorical Aspects of Differential and Difference Galois Theory (Invited Plenary Talk)

Title: Differentials Algebras in Differential Categories

[T.59] International Category Theory Conference (CT) 2025 (Invited Plenary Talk)

Title: Differential Graded Algebras in Differential Categories

[T.58] Foundational Methods in Computer Science (FMCS) 2025 (Invited Plenary Talk)

Title: Tutorial on Integrations and Rota-Baxter Algebras

[T.57] Canadian Mathematical Society (CMS) Summer Meeting 2025 -- Category Theory Scientific Session

Title: Cartesian Fermat Categories

[T.56] Workshop on Categorical Structures in Computer Science 2024 (Invited Plenary Talk)

Title: Traced Cartesian Differential Categories: Combining Fixpoints and Differentiation

[T.55] Category Theory Octoberfest 2024

Title: Additive Enrichment from Coderelictions

[T.54] Foundational Methods in Computer Science (FMCS) 2024 (Invited Plenary Talk)

Title: Drazin Inverses in Categories

[T.53] International Category Theory Conference (CT) 2024

Title: Free Differential Storage Modalities

[T.52] Mathematical Foundations of Programming Semantics (MFPS) 2024

Title: An Ultrametric for Cartesian Differential Categories for Taylor Series Convergence

[T.51] Applied Category Theory (ACT) 2024

Title: Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories

[T.50] Differential λ-Calculus and Differential Linear Logic, 20 Years Later (Invited Plenary Talk)

Title: Differential Categories

[T.49] Australian Mathematical Society Conference (AustMS) 2023 -- Category theory, Homotopy theory and K-theory Session (Invited Contributed Talk)

Title: Hopf Monads on Biproducts

[T.48] Australian Algebra Conference 2023

Title: Zinbiel Algebras and the Fundamental Theorems of Calculus

[T.47] Category Theory Octoberfest 2023

Title: Integrations in Differential Categories

[T.46] Quantum Physics and Logic (QPL) 2023

Title: Moore-Penrose Dagger Categories

[T.45] Logic in Computer Science (LICS) 2023

Title: Taylor Expansion as a Monad in Models of DiLL

[T.44] International Workshop on Quantitative Logical Methods (QUALOG) 2023 (Invited Contributed Talk)

Title: A Taylor Series Metric for Cartesian Differential Categories

[T.43] Mathematical Foundations of Programming Semantics (MFPS) 2023

Title: Cartesian Differential Kleisli Categories

[T.42] Conference on Algebra and Coalgebra in Computer Science (CALCO) 2023 -- Special Session on Category Theory in Machine Learning (Invited Plenary Talk)

Title: Differential Categories and Machine Learning

[T.41] Foundational Methods in Computer Science (FMCS) 2023

Title: Classical Distributive Restriction Categories

[T.40] Canadian Mathematical Society (CMS) Summer Meeting 2023 -- Hopf Algebra Scientific Session

Title: Lifting Trace with Hopf Algebras and Hopf Monads

[T.39] Computer Science and Categories (CSCAT) 2023

Title: Classical Distributive Restriction Categories

[T.38] KTGU Mathematics Workshop for Young Researchers (Invited Plenary Talk)

Title: Tangent Categories: A Bridge between Differential Geometry and Algebraic Geometry

[T.37] Workshop on Categorical Structures in Computer Science

Title: The Fundamental Theorems of Calculus and Zinbiel Algebras

[T.36] Category Theory Octoberfest 2022

Title: Uniqueness of Differentiation in Differential Categories

[T.35] Linearity and Trends in Linear Logic and its Applications (TLLA) 2022

Title: Copromotion and Taylor Approximation

[T.34] Applied Category Theory (ACT) 2022

Title: Monoidal Reverse Differential Categories

[T.33] Foundational Methods in Computer Science (FMCS) 2022 (Invited Plenary Talk)

Title: Tangent Categories and Algebraic Geometry

[T.32] 106th Peripatetic Seminar on Sheaves and Logic

Title: Algebraic Geometry and Tangent Categories

[T.31] Novemberfest 2021

Title: Hopf Monads and Traced Monads

[T.30] Conference on Algebra and Coalgebra in Computer Science (CALCO) 2021

Title: Coderelictions for Free Exponential Modalities

[T.29] International Category Theory Conference (CT) 2021

Title: Tensor Restriction Categories.

[T.28] International Conference on Applied Category Theory (ACT) 2021

Title: Jacobians and Gradients for Cartesian Differential Categories.

[T.27] Foundational Methods in Computer Science (FMCS) 2021

Title: Linearizing Combinators.

[T.26] Banff International Research Station (BIRS) Workshop on Tangent Categories and their Applications (Invited Plenary Talk)

Title: The World of Differential Categories: A Tutorial on Cartesian Differential Categories.

[T.25] Joint PPS - PIHOC - DIAPASoN Workshop 2021 (Invited Plenary Talk)

Title: Introduction to Reverse Derivative Categories.

[T.24] London Mathematical Society (LMS) Yorkshire and Midlands Category Theory Seminar (YAMCATS) Category Theory and its Applications Lecture Series

Title: The Theory of Differential Categories. (4 tutorial lectures)

[T.23] Oxford Quantum Group Workshop 2021

Title: What the heck is the reverse derivative?

[T.22] Yorkshire and Midlands Category Theory Seminar (YAMCATS) 2020 (Invited Plenary Talk)

Title: Characterizing Cofree Cartesian Differential Categories.

[T.21] Computer Science Logic (CSL) 2020

Title: Reverse Derivative Categories.

[T.20] Computer Science Logic (CSL) 2020

Title: Tangent Categories from the Coalgebras of Differential Categories.

[T.19] Postgraduate Conference in Category Theory and its Applications (PGR.CT) 2019

Title: Exponential Functions for Cartesian Differential Categories.

[T.18] International Category Theory Conference (CT) 2019

Title: Tangent Categories from the Coalgebras of Differential Categories.

[T.17] Quantum Physics and Logic (QPL) 2019

Title: Why FHilb is NOT an interesting (co)differential category.

[T.16] Canadian Mathematical Society (CMS) Summer Meeting 2019 -- Category Theory Scientific Session (Invited Contributed Talk)

Title: The Poincaré Lemma for Codifferential Categories with Antiderivatives.

[T.15] Foundational Methods in Computer Science (FMCS) 2019 (Invited Plenary Talk)

Title: Tutorials on differential categories and Cartesian differential categories.

[T.14] Category Theory Oktoberfest 2018

Title: Why FHilb is NOT an interesting differential category.

[T.13] Formal Structures for Computation and Deduction (FSCD) 2018

Title: Lifting Coalgebra Modalities and IMELL Model Structure to Eilenberg-Moore Categories.

[T.12] Mathematical Foundations of Programming Semantics (MFPS) 2018

Title: Cartesian Integral Categories and Contextual Integral Categories.

[T.11] Canadian Mathematical Society (CMS) Summer Meeting 2018 -- Category Theory Scientific Session (Invited Contributed Talk)

Title: Differential Categories and Representable Tangent Categories.

[T.10] Foundational Methods in Computer Science (FMCS) 2018

Title: A Tangent Alternative to the Faa Di Bruno Construction.

[T.9] ChoCoLa Meeting Spring 2018 (Invited Plenary Talk)

Title: Differential Algebras in Differential Categories.

[T.8] DuskoFest Workshop 2017

Title: The Story of Differential Categories

[T.7] Formal Structures for Computation and Deduction (FSCD) 2017

Title: There is only one notion of differentiation.

[T.6] Computer Science Logic (CSL) 2017

Title: Integral Categories and Calculus Categories.

[T.5] International Category Theory Conference (CT) 2017

Title: Integration for Tangent Categories.

[T.4] Foundational Methods in Computer Science (FMCS) 2017

Title: There is only one notion of differentiation.

[T.3] Union College Mathematics Conference 2016

Title: Introduction to Tensor Integral Categories.

[T.2] International Category Theory Conference (CT) 2016

Title: Introduction to Cartesian Integral Categories.

[T.1] Foundational Methods in Computer Science (FMCS) 2016

Title: Introduction to Monoidal Integral Categories.

Seminar Talks:

Research Seminar (April 2026), Research Institute of Mathematical Science, Kyoto Univeristy

Title: On Hassei’s Question about Traced Monoidal Closed Categories and Idempotent Comonads on Compact Closed Categories

Research Seminar (November 2025), Research Institute of Mathematical Science, Kyoto Univeristy

Title: Free Differential Modalities

Topology and Geometry Seminar (September 2025), Texas Tech University

Title: The world of differential categories

Maths and Stats Seminar (September 2025), Western Sydney University

Title: Fundamental Theorems of Calculus and Zinbiel Algebras

Australian Category Seminar (September 2025), Macquarie University

Title: From Moore-Penrose to Markov via Gauss

Algebra, Logic and Topology Seminar (August 2025), University of Coimbra

Title: Drazin inverses in (dagger) categories

Topos Institute Colloquium (June 2025), Topos Institute

Title: Cartesian Fermat Categories, a new class of Cartesian Differential Categories

Australian Category Seminar (May 2025), Macquarie University

Title: Introducing Cartesian Fermat Categories

Australian Category Seminar (May 2025), Macquarie University

Title: Dagger Drazin Inverses

Algebra and Topology Seminar (April 2025), Australian National University

Title: Tangent Categories - linking Differential Geometry and Algebraic Geometry

Australian Category Seminar (December 2024), Macquarie University

Title: Strict Monoids in Traced Monoidal Categories

Pure Math Seminar (September 2024), University of New South Wales

Title: The Fundamental Theorems of Calculus and Zinbiel Algebras

Seminar Geometric Methords in Mathematics (June 2024), Technische Universitat Dresden

Title: Tangent Categories

Seminar Geometric Methords in Mathematics (June 2024), Technische Universitat Dresden

Title: Lifting Trace with Hopf Algebras and Hopf Monads

Foundations Seminar (June 2024), Universita di Pisa

Title: Classical Distributive Restriction Categories

TSEM & TCAT Seminar (June 2024) Tallinn University of Technology

Title: Drazin Inverses in Categories

Online Category Theory Seminar (May 2024) Category Theory Zulip Forum

Title: A tour around the world of differential categories

Quantum Computation Structures Seminar (May 2024) Laboratoire Méthodes Formelles

Title: Tutorial on Differential Categories

Semantics Seminar (May 2024) Institut de Recherche en Informatique Fondamentale

Title: Free Differential Storage Modalities

Australian Category Seminar (April 2024), Macquarie University

Title: Drazin Inverses in Additive Categories and Fitting's Results

Australian Category Seminar (April 2024), Macquarie University

Title: On Leinster’s Eventual Image Duality (and the relation to Drazin inverses)

Australian Category Seminar (April 2024), Macquarie University

Title: Drazin Inverses in Categories

Algebra Seminar (March 2024), University of Sydney

Title: The Fundamental Theorems of Calculus and Zinbiel Algebras

Pure Mathematics Seminar (November 2023), Melbourne University

Title: Tangent Categories

Australian Category Seminar (October 2023), Macquarie University

Title: Derivations and Integrations in a Differential Category (with Antiderivatives)

Algebra Seminar (October 2023), University of Louisiana at Lafayette

Title: Classical distributive restriction categories

Australian Category Seminar (September 2023), Macquarie University

Title: Algebras of classified restriction categories

Australian Category Seminar (September 2023), Macquarie University

Title: Classical distributive restriction categories

Australian Category Seminar (May 2023), Macquarie University

Title: Traced monads and Hopf monads

Australian Category Seminar (May 2023), Macquarie University

Title: Moore-Penrose Dagger Categories

ERATO MMSD Colloquium (February 2023) National Institute of Informatics

Title: Moore-Penrose Dagger Categories

Research Seminar (February 2023), Nagoya University

Title: A tour around the world of differential categories

Research Seminar (July 2022), Kyushu University

Title: A tour around the world of differential categories

ERATO MMSD Colloquium (May 2022) National Institute of Informatics

Title: A tour around the world of differential categories

Research Seminar (April 2022), Research Institute of Mathematical Science, Kyoto Univeristy

Title: A tour around the world of differential categories

Atlantic Category Theory Seminar (January 2022), Dalhousie University

Title: Monoidal Closed but not Compact Closed

Peripatetic Seminar (October 2021), University of Calgary

Title: Building Cartesian Differential Categories as Kleisli Categories

Atlantic Category Theory Seminar (September 2021), Dalhousie University

Title: The Fundamental Theorems of Calculus and Zinbiel Algebras

Peripatetic Seminar (January 2021), University of Calgary

Title: Characterizing Cofree Cartesian Differential Categories

Semantics Seminar (December 2020) Institut de Recherche en Informatique Fondamentale

Title: On the coalgebras of a differential category and how to construct coderelictions from coalgebra structure

Category Theory Seminar (October 2020), University of Edinburgh

Title: Hopf Monads and Trace Monads

Logic Seminar (October 2020), University of Ottawa

Title: Exponential Functions in a Cartesian Differential Category

Peripatetic Seminar (July 2020), University of Calgary

Title: When is a Hopf Monad a Trace Monad?

Peripatetic Seminar (June 2020), University of Calgary

Title: Hyperbolic Functions for Cartesian Differential Categories

Peripatetic Seminar (April 2020), University of Calgary

Title: The symmetric algebra’s other universal properties

Research Seminar (March 2020), Research Institute of Mathematical Science, Kyoto Univeristy

Title: Introduction to Cartesian Differential Categories

Peripatetic Seminar (December 2019), University of Calgary

Title: Exponential Functions for Cartesian Differential Categories

Atlantic Category Theory Seminar (August 2019), Dalhousie University

Title: The Missing Link Between Hopf Monads and Star‑Autonomous Monads

Research Seminar (May 2019), Laboratories des Sciences du Numeriques de Nantes

Title: Introduction to Cartesian Differential Categories

Peripatetic Seminar (January 2019), University of Calgary

Title: Differential Algebras in Codifferential Categories

Category Theory Seminar (October 2020), University of Edinburgh

Title: Introduction to Differential Categories

Graduate Student Colloquium (October 2018), Kellogg College

Title: What is Category Theory?

Semantics Seminar (September 2018) Institut de Recherche en Informatique Fondamentale

Title: Differential Categories Revisited

Peripatetic Seminar (January 2018), University of Calgary

Title: Lifting Coalgebra Modalities

Peripatetic Seminar (July 2017), University of Calgary

Title: Integral Category Structure of Smooth Functions

Supervision:

Postdocs:

Marcello Lanfranchi, Macquarie University, (Feb 2025 -- On going)

PhD Students:

Isaiah Hilsenrath, University of Pennsylvania

PhD (Aug 2025 - On Going)

Jana Nickel, University of Hamburg

PhD (Oct 2025 - On Going)

Masters Students:

Svyatoslav Vorobyev, University of Sydney

Masters (Jan 2026 -- Dec 2026)

Jerry Zhang, University of New South Wales

Masters (Jan 2026 -- Dec 2026)

Joel Richarson, Macquarie University

Masters (Jan 2025 -- Dec 2025), Thesis: The Coalgebras of the Tangent Algebra Comonad

Undergraduate Students:

Xander James, Macquarie University

PACE Project (July-Nov 2026), Project: Research in Applied Category Theory

Bethi Banik, Macquarie University

Summer Vacation Research Project (Dec 2025-Jan 2026), Project: Moore-Penrose Inverses and Parallel Sum

Jack Kinder, Macquarie University

Summer Vacation Research Project (Dec 2025-Jan 2026), Project: Learning Reverse Differentiation

August Willoughby, Macquarie University

PACE Project (July-Nov 2026), Project: Research in Applied Category Theory

Summer Vacation Research Project (Dec 2025-Jan 2026), Project: Backprop as a functor for Cartesian Reverse Differential Categories

Semester Project (July-Nov 2025), Project: Backprop as a functor for Cartesian Reverse Differential Categories

Carlos Pascual Miralles, Macquarie University

Semester Project (Feb-May 2025), Project: Cartesian Fermat Categories

Aaron Biggin, Macquarie University

Software Engineering Research Thesis (July 2026 - June 2027), Thesis: Differential Lawvere Theories

PACE Project (July-Nov 2025), Project: Differential Lawvere Theories and Jacobians

Summer Vacation Research Project (Jan-Feb 2025), Project: Reverse Differentiation of Exponential Maps

Summer Vacation Research Project (Jan-Feb 2024), Project: Reverse Faà di Bruno's Formula for Cartesian Reverse Differential Categories

Visiting Graduate Students:

Thea Li, visiting PhD student from QUACS, INRIA (October 2026)
Ivan Schwieger, visiting PhD student from the University of Illinois Urbana-Champaign (July-Aug 2026)
Jean-Baptiste Vienney, visiting PhD student from the University of Ottawa (March 2026)
Chiara Sava, visiting PhD student from the Charles University (Feb-April 2025)
Rose Kudzman-Blais, visiting PhD student from the University of Ottawa (Nov 2024)
Nick Hu, visiting PhD student from University of Oxford (July 2024)
Marcello Lanfranchi, visiting PhD student from Dalhousie University (Feb-Mar 2024)

Visiting Postdocs:

Luca Mesiti, visiting postdoc from Stellenbosch University (January 2027)
Elena Caviglia, visiting postdoc from Stellenbosch University (January 2027)
Rose Kudzman-Blais, visiting postdoc from Kyoto University (October 2026)
Aymeric Walch, visiting postdoc from ISAE-Supaero (September 2026)
James Hefford, visiting postdoc from QUACS, INRIA (December 2025)
Cole Comfort, visiting postdoc from QUACS, INRIA (September 2025)
Geoff Vooys, visiting postdoc from the University of Calgary (November 2024)

Organizer, Chair, and Committee Roles:

Program Chair and/or Organizer:

Session on "Category Theory, Homotopy Theory, and K-Theory" at the Australian Mathematical Society Conference (AustMS) 2026
Differentiation in Category Theory and Program Semantics Workshop 2026
Session on "Category Theory, Homotopy Theory, and K-Theory" at the Australian Mathematical Society Conference (AustMS) 2025
"Mini Street-Fest", Special Australian Category Theory Seminar Day for Ross Street's 80th Birthday (Oct 2025)
Session on "Category Theory: Structures and Applications" at the Canadian Mathematical Society Summer Meeting (CMS) 2025
Eighth International Conference on Applied Category Theory (ACT) 2025
Workshop on Categorical Structures in Computer Science 2022
Third Symposium on Compositional Structures (SYCO3)

Program/Scientific Committee:

Seminar Organizer:

Pacific Category Theory Seminar (Dec 2025 -- Ongoing) (Online Monthly Research Seminar) (co-Founder)
Australian Category Theory Seminar (Aug 2024 -- Feb 2025) (Weekly Research Seminar)
Kellogg College Student Colloquium 2018/2019 (Weekly Graduate Student Seminar)
University of Calgary Mathematics Graduate Colloquium 2017/2018 (Weekly Graduate Student Seminar)

Award Committee:

Editorial Responsibilities:

Editor:

Proceedings of Eighth International Conference on Applied Category Theory in Electronic Proceedings in Theoretical Computer Science
Special issue of Mathematical Structures in Computer Science on "Differential Structures in Computer Science and Mathematics"

Academic Commitees and Responsiblities:

International Responsibilities:

Moderator of the international category theory mailing list (2023 - Ongoing)

National Responsibilities:

Australian Algebra Group Executive Committee (2026-2028)

Macquarie University:

FSE = Faculty of Science and Engineering

MAPS = School of Mathematical and Physical Sciences

MAPS Research Committee (2024 - On Going)
FSE-MAPS 2024-2025 Summer Research Internship Committee
MAPS First Aid Officer (2023 - On Going)

Teaching:

Macquarie University

Semester 1 2027:

Thesis Supervisor for COMP4093: Software Engineering Research Thesis B

Semester 2 2026:

Lecturer for MATH1020: Calculus and Linear Algebra II
Lecturer for MATH3030: Mathematics by Enquiry
Project Supervisor for MATH3599: PACE - Professional Practice for Mathematical Sciences
Thesis Supervisor for COMP4092: Software Engineering Research Thesis A

Semester 2 2025:

Project Supervisor for MATH3599: PACE - Professional Practice for Mathematical Sciences

Semester 1 2025

Unit Convenor and Lecturer for MATH3907: Algebra IIIA

Semester 1 2024

Lecturer for MATH3907: Algebra IIIA

University of Pennsylvania

Spring Semester 2026

Supervisor of reading course MATH8100 on Turing Categories

Fall Semester 2025

Supervisor of reading course MATH9999 on Differential Categories and Categorical Machine Learning

University of Oxford, New College

A college tutor is equivalent to a teaching assistant at other universities.

Hilary 2021

College Tutor for Categorical Quantum Mechanics

Michaelmas 2020

College Tutor for Homological Algebra

University of Oxford, Computer Science Department

A tutor is equivalent to a teaching assistant at other universities, while a teaching assistant is equivalent to a marker at other universities.

Hilary 2020

Lecturer for Categorical Quantum Mechanics

Michaelmas 2020

Tutor for Categories, Proofs and Processes
Tutor for Quantum Processes and Computation

University of Oxford, Mathematics Institute

A tutor is equivalent to a teaching assistant at other universities, while a teaching assistant is equivalent to a marker at other universities.

Michaelmas 2020

Tutor for Category Theory

Hilary 2019

Tutor for Set Theory (x2)

Hilary 2018

Teaching Assistant for Introduction to Quantum Information

Michaelmas 2018

Teaching Assistant for Logic

University of Calgary, Mathematics Department

Winter Semester 2017

Teaching Assistant for Vector Calculus for Eng. & Sci (x2)
Teaching Assistant for Calculus III
Marker for Analysis

Spring Semester 2016

Teaching Assistant for Linear Methods I (x2)
Teaching Assistant for Linear Methods II

Winter Semester 2016

Teaching Assistant for Linear Methods I (x2)
Drop-in Session Tutor for Discrete Math
Drop-in Session Tutor for Linear Algebra I

Fall Semester 2016

Teaching Assistant for Linear Methods I (x2)
Teaching Assistant for Linear Methods II (x2)
Drop-in Session Tutor for Linear Methods I

Fall Semester 2015

Teaching Assistant for Calculus I (x2)
Teaching Assistant for Linear Methods I (x2)
Drop-in Session Tutor for Calculus

University of Ottawa, Mathematics Department

Winter Semester 2015

Teaching Assistant for Calculus II

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