I am interested in duality theorems in arithmetics, and in their possible formulation as Pontryagin duality. Condensed Mathematics plays a key role in this topic, since it allows to give topological structures to algebraic invariants appearing in Arithmetic Geometry, e.g. cohomology groups.
In particular, during my Ph.D. I am studying a topologized version of the local Tate duality, which can take the form of a Pontryagin duality between locally compact abelian groups of finite ranks. For a more detailed discussion:
- My poster.
- My preprint, Duality for condensed cohomology of the Weil group of a p-adic field., https://arxiv.org/abs/2402.05565 (2024).
- My Master's Thesis, Condensed Mathematics: towards a rising theory, realised in spring 2021 at the Université de Bordeaux.
Talks
Some expository talks that I gave based on these topics.
Some expository talks that I gave based on these topics.
- Towards a new cohomology theory for p-adic fields, 2nd Algant Alumni Network Symposium (Saint-Jacut-de-la-Mer), October 2023. Slides of the talk.
- Exploring Geometric Intuition in Number Theory: the study of the Weil group , MARGAUx PhD Days 2023 (Poitiers), May 2023.
- What is Condensed Mathematics?, PhD Days (Milan), December 2021.
- Condensed Mathematics: exploring a rising theory, Lambda seminar (Bordeaux), October 2021.