Northern California Symplectic Geometry Seminar: Contact and symplectic foliations/Skeleta of Weinstein manifolds

Seminar | May 1 | 2:30-5 p.m. | Stanford University Mathematics Department, 384H/383N

 Alvaro del Pino/Laura Starkston, ICMAT, University of Madrid/Stanford University

 Department of Mathematics

Alvaro del Pino: A foliation is said to be symplectic if it admits a leafwise symplectic structure. One can further require this leafwise symplectic form to extend to a global closed 2-form; then we say that the symplectic foliation is strong. Similarly, one can define a contact foliation to be simply a foliation endowed with a leafwise contact structure.

In dimension 3, every foliation by orientable surfaces is symplectic, and being strong amounts to being taut. By work of Thurston, we know that constructing surface foliations in 3-manifolds is easy if we allow for the presence of Reeb components. It is also known that taut foliations are not as flexible and indeed they interact heavily with the topology of the ambient manifold.

In higher dimensions not much is known about the construction of (strong) symplectic foliations. I will review some of the literature in this direction, explaining also the situation in the contact case.

Laura Starkston: We will discuss the core isotropic skeleton of a Weinstein manifold, and see how this skeleton can change under homotopies of the Weinstein structure. A natural class of controlled singularities will typically appear in these skeleta which corresponds to Nadler's arboreal singularities. Our goal is to break up every other singularity which appears in the skeleton into a collection of these arboreal singularities.

Please contact to offer or request a ride.

There will be dinner following the talks.

D. Auroux, Y. Eliashberg, D. Fuchs, V. Ginzburg, M. Hutchings, E. Ionel, R. Montgomery, L. Starkston, K. Wehrheim, A. Weinstein