Séminaire Géométrie et applications

Michael Rothgang

Equivariant transversality for holomorphic curves

16 juin 2025 - 14:00Salle de séminaires IRMA

Consider closed holomorphic curves in symplectic $G$-manifolds, with respect to a $G$-invariant almost complex structure. We should not expect the moduli space of such curves to be a manifold (after all, transversality and symmetry are famously incompatible). However, we can hope for a clean intersection condition: the moduli space decomposes into countably many disjoint strata which are smooth manifolds, whose dimensions are explicitly computable.

I present this decomposition for simple curves, and indicate how to extend this to multiple covers. These are the first steps towards a well-behaved theory of equivariant holomorphic curves. This has applications to the 3-body problem and real Gromov-Witten theory.
Karin Melnick

Compact Lorentzian conformally flat manifolds

16 juin 2025 - 15:30Salle de séminaires IRMA

Any closed, flat Riemannian manifold is finitely covered by the torus, by Bieberbach's classical theorem. Similar classifications have been pursued for closed, Riemannian conformally flat manifolds, as well as for closed, flat Lorentzian manifolds. I will present the classification of closed, Lorentzian conformally flat manifolds with unipotent holonomy. This is joint work with Rachel Lee.
Victor Le Guilloux

à préciser

15 septembre 2025 - 15:30Salle de séminaires IRMA