Interplay between Quantitative Aspects of LCS Geometry and Contact Dynamics

par Pacôme van Overschelde (Université Libre de Bruxelles)

vendredi 10 avr. 2026, 11:15 → 12:15 Europe/Paris

112 (ICJ)

Locally conformally symplectic (LCS) structures are a generalization of symplectic structures, making them more abundant.  To an LCS form is associated a unique closed 1-form, called the Lee form. Historically, the most studied class of LCS structures is that of the first kind.

In this talk, we investigate quantitative properties of exact LCS manifolds, namely the homotheties of the Lee form that still produce an exact LCS form.  This leads to the notion of elasticity of an exact LCS pair, which provides a tool to study exact LCS manifolds that are not of the first kind, but whose behaviour remains close to it.

In the closed case, this allows us to characterize these LCS manifolds as precisely those that are isomorphic to the LCS mapping torus of a contactomorphism.  As a consequence, we obtain a lower bound on the maxima and an upper bound on the minima of the various conformal factors associated with a contactomorphism on a closed contact manifold.