Graduate student workshop in symplectic and contact geometry

Stanford University, Stanford CA

Investigators

Abstract

This National Science Foundation award provides partial support for a workshop to be held May 19-25, 2017 at Truckee, California. This workshop aims to introduce aspiring mathematicians in the fields of symplectic and contact geometry and from many institutions to vibrant areas of research, fostering collaboration, forming strong research ties between young researchers, and thus promoting future collaboration and research. The workshop is specifically designed to encourage the development of a diverse group of researchers in the fields of symplectic and contact geometry. It is a week-long intensive workshop, in which all activities occur under one roof. The lectures are delivered by the graduate student participants with the help of three mentors: Roger Casals (MIT), Laura Starkston (Stanford), and Steven Sivek (Bonn), who are emerging expert researchers in the field. This setup enhances communication skills, encourages active involvement or the participants and forging new collaborations. The topic of the 2017 workshop is symplectic fillings of contact manifolds, a topic with both a rich history and lots of new ideas that are currently being developed. One major aspect of the modern understanding of symplectic fillings is via an ever-growing dichotomy in symplectic and contact geometry: flexibility versus rigidity. Some fillings can be flexible, in which case they are completely determined up to isomorphism by differential-topological data; otherwise, there is a hope that some count of J-holomorphic curves implies that the symplectic geometry is more nuanced than the underlying differential topology. One goal of the workshop is to form bridges between these two different perspectives. Notes from the lectures and further information will be available on the website https://kylerec.wordpress.com/