The Arnold-Givental conjecture asserts that given a symplectic
manifold with an anti-symplectic involution, if the image of the
fixed-point locus under a Hamiltonian diffeomorphism intersect the
fixed-point locus transversely, them the number of...
What is a random Hamiltonian diffeomorphism? In this talk, we
propose an answer by constructing a family of probability measures
on the group Ham(M) of Hamiltonian diffeomorphisms of a closed
symplectic manifold M. We outline the construction, which...
We introduce the notion of a Penner-type class of an exact
symplectomorphism on a Liouville domain with an Ak-configuration of
Lagrangian spheres for k⩾2, and prove that such a class has
positive Floer-theoretic entropy. As a corollary, we
construct...
A symplectic manifold $M$ is called tame at infinity
if it admits a compatible almost complex structure such that the
corresponding Riemannian metric is complete and geometrically
bounded. Some such condition is necessary to
confine $J$-holomorphic...
Contact homeomorphisms are points in the closure of the
(compactly supported) contactomorphism group in the homeomorphism
group under the C0-topology. Recently, Dimitroglou Rizell and
Sullivan showed that the images of closed Legendrians under...
I will introduce microlocal sheaves on Weinstein manifolds and
survey recent results found in various papers of Laurent Côté,
Chris Kuo, Wenyuan Li, Vivek Shende, and myself.
In Euclidean spaces, star-shaped domains (also known as
Liouville domains) are fundamental objects in modern symplectic
geometry. Several important subclasses have been introduced and
studied, including dynamically convex domains, geometrically...
In this talk, I will describe the global dynamics of the spatial
isosceles three-body problem, using ideas from Embedded Contact
Homology. For energies below the critical level, the flow admits a
disk-like global surface of section bounded by the...
The theory of higher Reidemeister torsion yields characteristic
classes of (stable) fiber bundles of smooth manifolds. We use this
theory to define a new family of invariants for Legendrians in
1-jet spaces which we collectively call Legendrian...
A well-known result of Abouzaid says that the wrapped Fukaya
category of a cotangent bundle is generated by one cotangent fiber.
In the filtered case this is not true, but the filtered Fukaya
category comes with a notion of interleaving distance. We...
