The theory of persistence modules originated in topological data analysis and became an
active area of research in algebraic topology. This book provides a concise and self …

These notes give an introduction to embedded contact homology (ECH) of contact three-
manifolds, gathering together many basic notions which are scattered across a number of …

We use positive S 1–equivariant symplectic homology to define a sequence of symplectic
capacities ck for star-shaped domains in ℝ 2 n. These capacities are conjecturally equal to …

This paper calculates the function c (a) whose value at a is the infimum of the size of a ball
that contains a symplectic image of the ellipsoid E (1, a).(Here a≥ 1 is the ratio of the area of …

In this note we link symplectic and convex geometry by relating two seemingly different open
conjectures: a symplectic isoperimetric-type inequality for convex domains and Mahler's …

We use a neck stretching argument for holomorphic curves to produce symplectic disks of
small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive …

We show that every (possibly degenerate) contact form on a closed three-manifold has at
least two embedded Reeb orbits. We also show that if there are only finitely many …

In a previous paper, the second author used embedded contact homology (ECH) of contact
three-manifolds to define “ECH capacities” of four-dimensional symplectic manifolds. In the …

We survey some recent progress on understanding when one four-dimensional symplectic
manifold can be symplectically embedded into another. In 2010, McDuff established a …

Symplectic embedding problems, old and new Page 1 BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 55, Number 2, April 2018, Pages 139–182 …