Mathematics

I am specialised in the field of homotopy theory and algebra. My research focuses on higher structures that appear in algebra over chain complexes. I used to be a postdoc at the University of Utrecht in the team of Ieke Moerdijk. Before that, I was a PhD student at the University of Nice under the supervision of Bruno Vallette.

Articles

• From homotopy operads to infinity-operads in J. Noncommut. Geom., Journal (2017), Arxiv (2015).
• Homotopy theory of unital algebras in Algebraic and Geometric Topology Journal (2019), Arxiv (2016).
• Algebraic operads up to homotopy, submitted Arxiv (2017-2021).
• Homotopy Theory of linear coalgebras, with Damien Lejay, Arxiv (2018, first draft).
• Cubical model categories and quasi-categories, in Theory and Applications of Categories, Journal (2020), Arxiv (2018).
• Operads without coalgebras, with Damien Lejay, in Higher Structures, Journal, Arxiv (2019).
• Base change lax squares, with Damien Lejay, Arxiv (2020).
• Mapping Coalgebras I: Comonads, Arxiv (2020-2022).
• Presentations of algebras in chain complexes, Arxiv (2020).
• Localisation of cubical model categories, Arxiv (2021).
• An homotopical description of small presheaves, Arxiv (2021).
• Mapping coalgebras II: Operads, Arxiv (2022).
• A new approach to formal moduli problems, with Victor Roca i Lucio, Arxiv (2023).
• Homotopical operadic calculus in positive characteristic, with Victor Roca i Lucio, Arxiv (2023).
• Symmetric operads from a planar point of view, with Victor Roca i Lucio, Arxiv (2023).

To appear soon

• Mapping Coalgebras III: Chain complexes.
• Monadicity beyond reflexive coequalisers.
• Operads and algebras in categories.
• Machine learning in the lens of categories and props.
• The Segal formalism and the Boardman-Vogt constructions.
• Homotopy theory of linear coalgebras II: Examples with Damien Lejay.
• What is a cooperad with Damien Lejay.

Presentation notes

• Reminders on model categories (talk at a workshop on derived algebraic geometry in the mountains around Zurich in 2013) .
• An introduction to infinity-topoi (talk at our workshop on homotopy theory at Utrecht University in 2018) .
• Enrichissement en cogèbres (talk at LAGA Université Sorbonne Paris Nord in 2021) .
• Algèbres dans les complexes de chaînes et problèmes de modules formels (talk at Institut de Mathématiques Université Paul Sabatier Toulouse in 2024) .

Thesis

• Problèmes de déformation et algèbres de Lie différentielles graduées ; master thesis (2013).
• Théories homotopiques des algèbres unitaires et des opérades; PhD thesis (2016). HAL.

Projects

Many things to come...