Speaker: Michael Hutchings, UC Berkeley
Abstract:
We review various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. The results we will discuss can be proved using spectral invariants in embedded contact homology. Many of these results can also be proved using a new, simplified version of these invariants, called "elementary spectral invariants". The elementary spectral invariants are defined as a max-min energy of pseudoholomorphic curves satisfying certain constraints, inspired by a construction of McDuff-Siegel.
In the first lecture we will introduce the results on Reeb dynamics that we will be discussing. In the second lecture we will state the axiomatic properties of the elementary spectral invariants and explain how these can be used to obtain results on Reeb dynamics. In the third lecture we will describe the construction of elementary spectral invariants.
Lecture 1: Recent results in three-dimensional Reeb dynamics
Lecture 2: Elementary spectral invariants and applications
Lecture 3: Construction of elementary spectral invariants
