nLab J-B Vienney

Welcome to my webpage!

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.

My papers

1. Jean-Simon Pacaud Lemay, Jean-Baptiste Vienney, Graded Differential Categories and Graded Differential Linear Logic, MFPS2023, link
2. Jean-Baptiste Vienney, A bialgebraic characterization of symmetric powers in $\mathbb{Q}_{\ge 0}$-linear symmetric monoidal categories, ArXiv
3. Jean-Baptiste Vienney, An algebra modality admitting countably many deriving transformations, ArXiv
4. Jean-Baptiste Vienney, Extracting an $\mathbb{N}$-filtered differential modality from a differential modality, ArXiv

Work in progress, projects and ideas

1. Relative differential categories: replace the monad with a relative monad in the definition of a differential category. Status on 13 February 2024: will finish to write this after the extracting paper.

2. Glueing an $\mathbb{N}$-filtered differential modality into a differential modality. Status on 13 February 2024: did not start to write but I think it’s going to work fine quickly.

3. Hasse-Schimdt differential categories: replace usual differentiation by Hasse-Schmidt differentiation in the notion of a differential category. Status on 13 February 2024: will work on this once the extracting paper is finished. The higher-order rules from the extracting paper are needed to write down the definition of an Hasse-Schmidt differential category.

4. Higher-order tangent categories: a categorical framework for higher-order tangent bundles similar to tangent bundle categories. Status on 13 February 2024: keeping this for later — when I’ll start to work seriously on tangent categories.

5. Free divided power algebra, polynomial laws and differential categories: Is the free divided power algebra in the symmetric monoidal category of modules over a commutative rig a differential modality? Do modules over a commutative rig and polynomial laws between them form a cartesian differential category?

category: people