From the 1 of 6 linked papers with an AI index.
6 papers
The symplectic Hadamard question
Dan Cristofaro-Gardiner
The paper proves that any simply connected symplectic manifold that admits a complete compatible metric with nonpositive curvature is symplectomorphic to Euclidean space ℝ^{2n} wit…
Curvy points, the perimeter, and the complexity of convex toric domains
Dan Cristofaro-Gardiner, Nicki Magill, Dusa McDuff
We study the related notions of curvature and perimeter for toric boundaries and their implications for symplectic packing problems in dimension 4; a natural setting for this is a…
Topological symplectic manifolds and bi-Lipschitz structures
Dan Cristofaro-Gardiner, Boyu Zhang
We show that a topological symplectic manifold has a canonically associated bi-Lipschitz structure. As a corollary, we obtain the first examples of non-existence and non-uniqueness…
Symplectic Weyl Laws
Dan Cristofaro-Gardiner
We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. W…
Low-dimensional topology and symplectic dynamics
Dan Cristofaro-Gardiner
These are notes to accompany my lectures at the "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our u…
Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces
Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
This paper continues the study of link spectral invariants on compact surfaces, introduced in our previous work and shown to satisfy a Weyl law in which they asymptotically recover…