I’m a postdoctoral researcher at Institut de Recherche en Informatique Fondamentale (IRIF), working under Paul-André Melliès as part of the Malinca project. I completed my PhD in mathematics at Laboratoire Paul Painlevé under the supervision of Benoit Fresse.
Contact
IRIF Office 4029A
Mail despalungue @ irif . fr
Research Interests
Operads – Category Theory – \(E_n\)-Structures – Foundations of Mathematics
My research lies at the interface of category theory, logic, and algebraic topology. The purpose of my thesis was to construct cofibrant models of \(E_n\)-operads governing the structure of \(n\)-fold iterated monoidal categories. My work on internal structures suggested an approach to the formalisation of mathematical language, structured around the hierarchy of \(n\)-categories and supporting iterated internalisations. I am working to make this language logically rigorous, with the long-term aim of developing a proof assistant.
Publications
- PhD Thesis: Operads in 2-categories and models of structure interchange, 2024
(Currently turning the thesis results into articles)
Talks
- Towards an internal construction of meaning, Synthetic mathematics, logic-affine computation and efficient proof systems, CIRM, 09/2025 [ abstract – slides – video]
- Category Theory within a 2-category: internal enrichment, presheaf objects (and convolution products), CT2025, Brno, 07/2025 [ abstract – slides ]
- Category Theory within a 2-category: internal enrichment, presheaf objects and convolution products, Séminaire Itinérant de Catégories, Lens, 06/2025 [ abstract – slides ]
- Building all of mathematics without axioms: an \(n\)-categorical manifesto, New York City Category Theory Seminar, online, 03/2025 [ abstract – slides – video ]
- Generalised operads for multi-dimensional algebra, ALPE Seminar, Montpellier, 03/2024 [ abstract ]
- A tensor product for the interchange of categorical operads, Workshop on Homology of Configuration Spaces and related topics, Paris, 05/2023 [ abstract ]
- Boardman-Vogt tensor product of operads and interchange of \(E_n\)-structures, Séminaire de Topologie IMJ-LAGA, Paris, 02/2023 [ abstract ]
- Internal pseudomonoidal structures and Day convolution in a monoidal \(2\)-category, ItaCa, Pise, 12/2022 [ abstract – slides – video ]