nLab J-B Vienney

I’m a French math/computer science student. I finished my masters program as a visitor in Ottawa under the supervision of Rick Blute and Phil Scott and I now continue with them as a PhD student.

I’m interested by the logical approach to differentiation through differential linear logic and differential categories. My work currently tries to combine ideas from these fields with the notion of graded modality to clarify the functioning of ubiquitous functors in mathematics such as symmetric, exterior, divided powers or homology functors.

More broadly, I’m driven by the idea of making some algebraic concepts from mathematics into category theory and proof theory and make everything live together in the neatest way, allowing a computational interpretation, a logical analysis, and a maximal generalization of these algebraic concepts while at the same time creating new insights into pure proof theory that will be usable in a more computer-science oriented perspective (eg. I first encountered graded Seely isomorphisms as properties of polynomial algebras before understanding that they are a distinctive feature of graded differential linear logic).

I like the insights given by the philosophy of Ludwig Wittgenstein and think they are a useful inspiration for research in mathematics and computer science. At least they are for me although I’m not a philosopher and so I am not able to formalize very precisely my feelings on this. But it does play a role in my thoughts, let’s say that I’m inspired by this philosophy.

Projects

I currently work on this stuff:

• Graded differential linear logic and graded differential categories (with Jean-Simon Lemay) which index the exponential modality of differential linear logic or differential categories by any rig.
• Higher-order differential linear logic and higher-order differential categories which replace differentiation by Hasse-Schmidt differentiation.
• A string-diagrammatic calculus for symmetric powers based on an algebraic characterization of symmetric powers in symmetric monoidal $\mathbb{Q}^{+}$-linear categories.
• Graded kinds of Seely isomorphism.

A next goal is:

• Make Schur functors, which are usually used in representation theory of the symmetric group, into string diagrams and/or linear logic by using an exponential modality graded by Young diagrams.

Papers

• Jean-Simon Pacaud Lemay, Jean-Baptiste Vienney, Graded Differential Categories and Graded Differential Linear Logic, 2023, Preprint, arXiv

Presentations

… to come (I will add some slides/videos soon) …

category: people