The double bubble plumbing, first studied by Smith and Wemyss,
is a Stein neighborhood of two Lagrangian 3-spheres intersecting
cleanly along an unknotted circle in some 6-dimensional symplectic
manifold. Depending on the identification of the...
The parametrised Whitehead torsion is an invariant of families
of manifolds, and can be viewed as a map to an algebraic K-theory
space. A strong version of the nearby Lagrangian conjecture says
that when applied to families of closed exact...
We will explore certain $C^0$-rigidity and flexibility phenomena
in the study of contact transformations. In particular, we will
show how the dichotomy between contact squeezing and non-squeezing
is related to the Rokhlin property of the group of...
We will outline the proof of an intersection result between
embedded Lagrangian tori and certain 1 parameter families of
product Lagrangian tori in the 4 dimensional symplectic cylinder.
The theorem can be applied to give new computations of the...
In this talk, I will construct an S1-equivariant version of the
relative symplectic cohomology developed by Varolgunes. As an
application, I will construct a relative version of Gutt-Hutchings
capacities and a relative version of symplectic (co...
The (small) quantum connection is one of the simplest objects
built out of Gromov-Witten theory, yet it gives rise to a
repertoire of rich and important questions such as the Gamma
conjectures and the Dubrovin conjectures. There is a very
basic...
The rectangular peg problem, an extension of the square peg
problem, is easy to outline but challenging to prove through
elementary methods. In this talk, I discuss how to show the
existence and a generic multiplicity result assuming the
Jordan...
We explore the construction of non-Weinstein Liouville geometric
objects based on Anosov 3-flows, introduced by Mitsumatsu, in the
generalized framework of Liouville Interpolation Systems and
non-singular partially hyperbolic flows. We discuss the...
We will present two results in complex geometry: (1) A Kähler
compactification of ℂn with a smooth divisor complement must be ℙn,
which confirms a conjecture of Brenton and Morrow under the Kähler
assumption; (2) Any complete asymptotically conical...
