Embedded contact homology (ECH) is a diffeomorphism invariant of
three-manifolds due to Hutchings, defined using a contact form.
This very diffeomorphism invariance makes it quite useful when
studying contact dynamics, because it is possible to...
In this talk I will discuss a Bennequin type inequality for
symplectic caps of S3 with standard contact structure. This has
interesting applications which can help us to understand the smooth
topology of symplectic caps and smoothly embedded suraces...
I will first give an overview of ECH. Then I will describe how
to compute ECH in the Morse-Bott setting a la Bourgeois. I will
discuss some classes of examples where this approach works. Finally
I will sketch the gluing results that allow us to...
I will explain a construction of a Legendrian version of
embedded contact homology (ECH) for a sutured contact manifold Y
along with a collection of Legendrians L contained in the boundary.
The chain complex is generated by sets of Reeb orbits and...
Localization is an important construction in algebra and
topology that allows one to study global phenomena a single prime
at a time. Flexibilization is an operation in symplectic topology
introduced by Cieliebak and Eliashberg that makes any two...
We will discuss the existence of rational (multi)sections and
unirulings for projective families f:X→CP1 with at most two
singular fibres. In particular, we will discuss two ingredients
that are used to construct the above algebraic curves. The...
We will discuss the first steps in an approach to proving
homological mirror symmetry for Looijenga pairs through tropical
Lagrangian sections. Namely, we will see how to construct these
Lagrangian sections from tropical data corresponding to line...
