Exact Lagrangians in Cotangent Bundles with Locally Conformally Symplectic Structure
Time: 2025-10-15
Published By: He Liu
Speaker(s): Adrien Currier(BICMR)
Time: 15:00-17:00 October 24, 2025
Venue: Room 77201, Jingchunyuan 78, BICMR
First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic geometry which allows for the study of Hamiltonian dynamics on a wider range of manifolds while preserving the local properties of symplectic geometry. After a long period of hibernation (especially as far as the topological aspect is concerned), this topic has recently seen renewed interest. However, to this day, the field of LCS topology remains vastly unexplored.
In this talk, we will introduce the various objects of LCS geometry and their behavior through both definitions and examples. We will then explore some quirks of this generalization through the lens of the nearby Lagrangian conjecture. And, finally, we will provide a partial answer to the question: when is an exact (LCS) Lagrangian homotopy equivalent to the zero-section?
