My work focuses on the computational content of deductive systems, from the perspective of graphical deduction systems.
Currently, I am exploring the geometric structure of cells in higher categories from a computational perspective. Higher categories are rich algebraic objects: n-dimensional cells can be composed in n different ways, which are related via the exchange law. We still know little about the computational complexity of the resulting theory. My work focuses on the word problem for these structures, which was studied first by Makkai in 2005. I am reusing notions from low-dimensional algebra (such as rewriting systems or automatic structures) and adapt them to this higher-dimensional version.
My long term goal is to apply diagrammatic reasoning to Export-Transform-Load systems such as OpenRefine. These systems have a notion of operation (atomic change in a database column) which is very well captured by symmetric monoidal theories. Modelling series of operations as morphisms in a finitely presented category would be very useful, for instance to analyze data flows during the transformations, allowing to rearrange a workflow without changing its effects on the data. Other open source projects can be found on my GitHub profile.
I started my DPhil in October 2016, under the supervision of Jamie Vicary.
Before that, I studied at École Normale Supérieure, in Paris. For my masters degree in mathematical logic and foundations of computer science, I took a research placement at the University of Ljubljana where I worked with Alex Simpson on algorithmic randomness and point-free topology.
Normal forms for planar connected string diagrams
Antonin Delpeuch and Jamie Vicary
In CoRR. Vol. abs/1804.07832. 2018.
Complexity of Grammar Induction for Quantum Types
In Electronic Proceedings in Theoretical Computer Science. Vol. 172. Pages 236–248. December, 2014.
From Natural Language to RDF Graphs with Pregroups
Antonin Delpeuch and Anne Preller
In Proceedings of the EACL 2014 Workshop on Type Theory and Natural Language Semantics (TTNLS). Pages 55–62. Gothenburg‚ Sweden. April, 2014. Association for Computational Linguistics.