Titre: FOUVRY - 73
Week 1-2 (17 August- 28 August 2026): Summer school
Week 3 (31 August -4 September 2026): Workshop
Week 4 (7-11 September 2026): Scientific collaborations
General summary:
The notion of duality in physics has a rich history, going back at least as far as the observation that Maxwell’s theory of elctromagnetism is symmetric after swapping electric and magnetic fields. More generally, dualities in physics can provide a way of relating two seemingly very different physical theories via a nontrivial duality transformation. For instance, S-duality in physics provides a way to swap strongly coupled physical theories for weakly coupled ones [MO77], for which we may use perturbative methods to exactly solve the equations governing the system.
New trends and applications around generalized Fokker-Planck operators This 4-weeks scientific program will be oriented around four related topics: 1. Witten and Bismut deformations of Hodge theory on Riemannian manifolds; 2. Persistent homology and Witten Laplacians; 3. Hypoellipticity and polynomes of vector fields; 4. Applications to molecular dynamics algorithms.
The aim of this programme is to break new ground in the arithmetic theory of K3 surfaces and closely related varieties (e.g., Enriques and elliptic surfaces; hyper-Kähler varieties), capitalising on a web of recent advances and conjectural frameworks. Progress on the arithmetic of K3 surfaces will likely have important consequences for more general questions about Shimura varieties, abelian and hyper-Kähler varieties, their rational and algebraic points. The programme consists of 5 weeks of research collaborations (working groups, research seminars) capped off by a one week workshop.