JS Pacaud Lemay

Jean-Simon Pacaud Lemay

Doctoral Student

Student, Kellogg College

Leaving date: 30th April 2021

Biography

Personal Webpage: https://sites.google.com/view/jspl-personal-webpage/

Email: jean-simon.lemay@kellogg.ox.ac.uk

Office: Computer Science Department, Room 251

I also do some teaching for the Mathematical Institute: https://www.maths.ox.ac.uk/people/jean-simon.lemay

Journal Papers:

Differential Equations in a Tangent Category I: Complete vector fields, flows, and exponentials. Cockett, R., Cruttwell, G., Lemay, J-S. P. (2021). Applied Categorical Structures. (pdf)
Exponential Functions for Cartesian Differential Categories. Lemay, J-S. P. (2020). Applied Categorical Structures. (site)(pdf)
Integral and differential structure on the free C-infinity ring modality. Cruttwell, G., Lemay, J-S. P., Lucyshin-Wright R. (2020). Cahiers de topologie et géométrie différentielle catégoriques (pdf)
Convenient Antiderivates for Differential Linear Categories. Lemay, J-S. P. (2020). Mathematical Structures in Computer Science. (site)(pdf)
Differential Categories Revisited. Blute, R., Cockett, R., Lemay, J-S. P., & Seely R.A.G. (2019). Applied Categorical Structures. (site)(pdf)
Lifting Coalgebra Modalities and MELL Model Structure to Eilenberg-Moore Categories. Lemay, J-S. P. (2019). Logical Methods in Computer Science. (site)(pdf)
Differential Algebras in Codifferential Categories. Lemay, J-S. P. (2019). Journal of Pure and Applied Algebra. (site) (pdf)
Linear Distributivity with Negation, Star-Autonomy, and Hopf Monads. Hasegawa, M. & Lemay, J-S. P. (2018) Theory and Applications of Categories. (site)(pdf)
A Tangent Category Alternative to the Faa di Bruno Construction. Lemay, J-S. P. (2018). Theory and Applications of Categories. (site)(pdf)
Integral Categories and Calculus Categories. Cockett, R., & Lemay, J-S. P. (2018). Mathematical Structures in Computer Science. (site)(pdf)

Preprints:

Cartesian Difference Categories. Alvarez-Picallo, M. & Lemay, J-S. P. (2020). (pdf)
Linearizing Combinators. Cockett, R., Lemay, J-S. P. (2020). (pdf)
Tensor-Restriction Categories. Heunen, C., Lemay, J-S. P. (2020). (pdf)
Cartesian Differential Categories as Skew-Enriched categories. Garner, R., Lemay, J-S. P. (2020). (pdf)

Conference Papers:

Cartesian Difference Categories. Alvarez-Picallo, M. & Lemay, J-S. P. FOSSACS 2020 (pdf)
Tangent Categories from the Coalgebras of Differential Categories. Cockett, R., Lemay, J-S. P., Lucyshyn-Wright, R. CSL 2020 (pdf)
Reverse Derivative Categories. Cockett, R., Cruttwell, G., Gallagher, J., Lemay J-S. P., MacAdam B., Plotkin G., & Pronk, D. CSL 2020 (pdf)
Why FHilb is NOT an interesting (co)differential category. Lemay J-S. P. QPL 2019 (pdf)
Higher order distributions for differential linear logic. Kerjean M., & Lemay J-S. P. FOSSACS 2019 (pdf)
Lifting Coalgebra Modalities and IMELL Model Structure to Eilenberg-Moore Categories. Lemay, J-S. P. FSCD 2018 (pdf)
Cartesian Integral Categories and Contextual Integral Categories. Cockett, R., & Lemay, J-S. P. MFPS 2018 (pdf)
There is only one notion of differentiation. Cockett, R., & Lemay, J-S. P. FSCD 2017 (pdf)
Integral Categories and Calculus Categories (Extended Abstract). Cockett, R., & Lemay, J-S. P. CSL 2017 (pdf)
The Shuffle Quasimonad and Modules with Differentiation and Integration. Bagnol, M., Blute, R., Cockett, R., & Lemay, J-S. P. MFPS 2016 (pdf)

Conference Presentations:

PPS - PIHOC - DIAPASoN Workshop 2021 (site): An introduction to reverse differential categories. (Invited Talk)
LMS YaMCATS Category Theory and its Applications Lecture Series (site): The Theory of Differential Categories (4 Lectures)
YAMCATS 2020 Meeting 22 (site): Characterizing Cofree Cartesian Differential Categories
CSL 2020 (site): Tangent Categories from the Coalgebras of Differential Categories.
CSL 2020 (site): Reverse Derivative Categories.
PGR.CT 2019 (site): Exponential Functions for Cartesian Differential Categories.
CT 2019 (site): Tangent Categories from the Coalgebras of Differential Categories.
QPL 2019 (site): Why FHilb is NOT an interesting (co)differential category.
CMS Summer Meeting 2019 (site): The Poincaré Lemma for Codifferential Categories with Antiderivatives (Invited Talk)
FMCS 2019 (site): Tutorials on differential categories and Cartesian differential categories (Invited Talk)
Category Theory Oktoberfest 2018 (site): Why FHilb is NOT an interesting differential category.
FSCD 2018 (site): Lifting Coalgebra Modalities and IMELL Model Structure to Eilenberg-Moore Categories.
MFPS 2018 (site): Cartesian Integral Categories and Contextual Integral Categories.
CMS Summer Meeting 2018 (site): Differential Categories and Representable Tangent Categories. (Invited Talk)
FMCS 2018 (site): A Tangent Alternative to the Faa Di Bruno Construction.
ChoCoLa Meeting April 2018 (site): Differential Algebras in Differential Categories. (Invited Talk)
FSCD 2017 (site): There is only one notion of differentiation.
CSL 2017 (site): Integral Categories and Calculus Categories.
CT 2017 (site): Integration for Tangent Categories.
FMCS 2017 (site): There is only one notion of differentiation.
Union College Mathematics Conference 2016 (site): Introduction to Tensor Integral Categories.
CT 2016 (site): Introduction to Cartesian Integral Categories.
FMCS 2016 (site): Introduction to Monoidal Integral Categories.

Conference Organizations & Commitees:

Local Organizer:

SYCO 3 (site)(Local Chair)

Progamme Committee:

SYCO 5 + STRING 3 (site)
SYCO 3 (site)

Research Visits:

Kyoto University, working with Masahito Hasegawa -- March, April, & May 2020
Mount Allison University , working with Geoff Cruttwell -- August 2019
University of Calgary , working with Robin Cockett and Kristine Bauer -- June 2019
Inria Nantes , working with Marie Kerjean -- May 2019
University of Edinburgh , working with Robin Cockett and Chris Heunen -- November & December 2018
IRIF , working with Christine Tasson , Marie Kerjean , Zeinad Galal , and Thomas Ehrhard -- September 2018
Mount Allison University , working with Geoff Cruttwell and Rory B. B. Lucyshyn-Wright -- May 2018
IRIF , working with Christine Tasson , Marie Kerjean , Zeinad Galal , and Thomas Ehrhard -- April 2018
University of Calgary , working with Robin Cockett and Kristine Bauer -- January 2018
Mount Allison University , working with Geoff Cruttwell and Rory B. B. Lucyshyn-Wright -- June 2017

Education:

Master of Science (M.Sc.) in Pure Mathematics

University of Calgary , Calgary, Alberta, Canada
Thesis: Integral and Calculus Categories
Supervisors: Professor Robin Cockett and Professor Kristine Bauer

Honours Bachelor of Science (B.Sc.) in Mathematic

University of Ottawa , Ottawa, Ontario, Canada
Supervisors: Professor Richard Blute and Professor Pieter Hofstra

Teaching:

University of Oxford, Mathematics Institute:

Hilary 2021: New College Tutor (for Tsinghua visiting students) for "Categorical Quantum Mechanics"
Michaelmas 2020: Tutor for "Category Theory", "Categories, Proofs and Processes", "Quantum Processes and Computation"
Michaelmas 2020: New College Tutor (for Tsinghua visiting students) for "Homological Algebra"
Hilary 2020: Lecturer for "Categorical Quantum Mechanics"
Hilary 2019: Tutor for "Set Theory" (x2)
Hilary 2018: TA for "Introduction to Quantum Information"
Michaelmas 2018: TA for "Logic"

University of Calgary, Mathematics Department:

Winter 2017: TA for "Vector Calculus for Eng. & Sci" (x2) and "Calculus III", and Marker for "Analysis"
Winter 2016: TA for "Linear Methods I" (x2), and Drop-in Sessions for "Discrete Math" and "Linear Algebra I"
Spring 2016: TA for "Linear Methods I" (x2) and "Linear Methods II"
Fall 2016: TA for "Linear Methods I" (x2) and "Linear Methods II" (x2), and Drop-in Sessions for "Linear Methods I"
Fall 2015: TA for "Calculus I" (x2) and "Linear Methods I" (x2), and Drop-in Sessions for "Calculus"

University of Ottawa, Mathematics Department:

Winter 2015: TA for "Calculus II"

Activities

Quantum Group

Supervisor

Jamie Vicary