nLab J-B Vienney

I’m a French math PhD student at the University of Ottawa. My supervisor is Rick Blute. Phil Scott was also my supervisor.

I’m interested in the logical approach to differentiation through differential linear logic and differential categories. I like trying to combine ideas from this field with the notion of graded modality to talk about ubiquitous functors in mathematics such as symmetric, exterior, divided powers or homology functors.

More broadly, I’m driven by the idea of turning some algebraic concepts from mathematics into category theory and proof theory and make everything live together in the neatest way.

I like the philosophy of Ludwig Wittgenstein and think that it is a useful inspiration for research in mathematics and computer science.

Projects

I wrote papers on:

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

I’m working on:

• Several little projects related to graded differential categories and symmetric powers in additive symmetric monoidal categories.
• Higher-order tangent categories which are a categorical framework for higher-order tangent bundles similar to tangent bundle categories.
• Hasse-Schimdt differential categories which replace usual differentiation by Hasse-Schmidt differentiation in the notion of differential category.

Papers

• Jean-Simon Pacaud Lemay, Jean-Baptiste Vienney, Graded Differential Categories and Graded Differential Linear Logic, MFPS2023, link
• Jean-Baptiste Vienney, String diagrams for symmetric powers I: In symmetric monoidal $\mathbb{Q}_{\ge 0}$-linear categories, preprint, ArXiv

category: people