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 is very useful, for instance to analyze data flows during the transformations, allowing to rearrange a workflow without changing its effects on the data. I am working towards implementing this in OpenRefine. Other open source projects can be found on my GitHub profile.
- Antonin Delpeuch, The word problem for double categories, working preprint. arXiv:1907.09927
- Antonin Delpeuch, A complete language for faceted dataflow programs, Applied Category Theory 2019, arXiv:1906.05937
- Antonin Delpeuch, Autonomization of monoidal categories, Applied Category Theory 2019, arXiv:1411.3827
- Antonin Delpeuch, A survey of OpenRefine reconciliation services, working preprint. arXiv:1906.08092
- Antonin Delpeuch and Jamie Vicary, Normal forms for planar connected string diagrams, Workshop on Higher Dimensional Rewriting and Applications, FLOC, Oxord, 7 July 2018, arXiv:1804.07832
- Antonin Delpeuch, Complexity of Grammar Induction for Quantum Types,Electronic Proceedings in Theoretical Computer Science. Vol. 172. Pages 236–248. December, 2014. DOI 10.4204/eptcs.172.16, arXiv:1404.3925
- Antonin Depleuch, Type-driven distributional semantics for prepositional phrase attachment, Master's thesis at the University of Cambridge, DOI 10.5281/zenodo.1299049
- Antonin Delpeuch and Anne Preller, From Natural Language to RDF Graphs with Pregroups, 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. DOI 10.3115/v1/w14-1407
- The word problem for double categories, Postgraduate Conference in Category Theory and Its Applications, University of Leicester, 18-19 November 2019
- Décider l'égalité de diagrammes de cordes (Decidability of equality for string diagrams), Catégories supérieures, polygraphes et homotopie, IRIF, Université Paris 7, 6 April 2018
- Schema alignment for Wikibase in OpenRefine, Harnessing open data for Monitoring and Evaluation workshop, European Research Council Executive Agency, Berlin, 17-19 June 2018
- 28th Computer Science Logic conference, reviewer
- 5th Symposium on Compositional Structures and 3rd Workshop on String Diagrams in Computation, Logic and Physics, PC member
- 3rd Symposium on Compositional Structures, PC member and local organizer
- 14th International Workshop on Coalgebraic Methods in Computer Science, reviewer
- 1st Symposium on Compositional Structures, reviewer
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.
The Word Problem for Double Categories
In arXiv:1907.09927 [cs‚ math]. July, 2019.
Autonomization of Monoidal Categories
In Proceedings of Applied Category Theory 2019. July, 2019.
A Complete Language for Faceted Dataflow Programs
In arXiv:1906.05937 [Cs‚ Math]. Oxford. June, 2019.