Low-dimensional topology and symplectic dynamics
Symplectic Geometry
2025-10-10 v1 Dynamical Systems
Abstract
These are notes to accompany my lectures at the "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems, using in part some tools from low-dimensional topology. In these notes, I try to give a sense for how this works by discussing a few examples from problems I have worked on and surveying some related developments. Some symplectic variants of Weyl's law play a key role. I also briefly comment on some other developments and on the relationship with what is known in higher dimensions. The lectures themselves are available online.
Cite
@article{arxiv.2510.07680,
title = {Low-dimensional topology and symplectic dynamics},
author = {Dan Cristofaro-Gardiner},
journal= {arXiv preprint arXiv:2510.07680},
year = {2025}
}