Berlin-Hamburg-Hannover-Seminar am 14.11.2025

Noah Porcelli (MPI Bonn) Bordism from quasi-isomorphism

The Fukaya category detects lots of topological infomation, both intrinsic and extrinsic, about (closed, exact) Lagrangians: such as their cohomology ring (intrinsic) and their fundamental class in the ambient symplectic manifold (extrinsic). I'll explain why it also detects bordism-theoretic infomation, with applications to studying nearby Lagrangians. This involves using a spectral Fukaya category, and using obstruction theory to ''lift'' an equivalence from the ordinary to the spectral world. Based on joint work with Ivan Smith.

Oliver Edtmair (ETH Zürich) On the topological invariance of helicity

Helicity is an invariant of divergence free vector fields on a three-manifold. One of its fundamental properties is invariance under volume preserving diffeomorphisms. Arnold, having derived an ergodic interpretation of helicity as an asymptotic Hopf invariant, asked whether helicity remains invariant under volume preserving homeomorphisms, and more generally, whether it admits an extension to topological volume preserving flows. In this talk, I will present an affirmative answer to both questions for non-singular flows. The proof draws on recent advances in C⁰ symplectic geometry, in particular regarding the algebraic structure of the group of area preserving homeomorphisms, which I will also survey. This is based on joint work with Sobhan Seyfaddini.