Student workshop in symplectic and contact geometry

Stanford University, Stanford CA

Investigators

Abstract

This award provides support for the next three editions of the Kylerec Student Workshop (2020, 2021 and 2022), starting with its 2020 edition to be held from July 20 to July 24 in Big Bear Lake, CA. The Kylerec 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 to four mentors, who are emerging expert researchers in the field. This setup enhances communication skills, encourages active involvement of the participants and forging new collaborations. The student organizers for the 2020 Kylerec workshop are Orsola Capovilla-Searle (Duke University), Dahye Cho (Stony Brook University), Francois-Simon Fauteux-Chapleau (Stanford University), Tim Large (MIT) and Sarah McConnell (Stanford University). The topic is Quantitative Symplectic Geometry, with a focus on symplectic embedding problems. The deceptively simple question of when does one symplectic manifold embed inside another, and the subtle dependance of this question on quantitative parameters, has been a focal point of the subject for the last thirty years. Since Gromov's celebrated non-squeezing result, a variety of techniques drawing upon ideas in dynamical systems, toric algebraic geometry and four-dimensional gauge theory have been used to better understand such problems; yet a systematic understanding has eluded researchers thus far. The objective of the 2020 Kylerec workshop is to understand the current state of knowledge on such questions, covering both the methods researchers have developed to produce surprising symplectic embeddings, as well as the technical tools of Floer theory and embedded contact homology that have been used to provide state-of-the-art obstructions to the existence of a symplectic embedding. The web site for the Kylerec workshops is https://kylerec.wordpress.com/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.