I will present two constructions of Kähler manifolds, endowed
with Hamiltonian torus actions of infinite dimension. In the first
example, zeroes of the moment map are related to isotropic maps
from a surfaces in ℝ2n. In the second example, which is...
I will discuss joint work with McLean and Smith, lifting the
results of Seidel, Lalonde, McDuff, and Polterovich concerning the
topology of Hamiltonian fibrations over the 2-sphere from rational
cohomology to complex cobordism. In addition to the...
The topic of the talk will be Floer theories on exact symplectic
orbifolds with smooth contact boundary. More precisely, I will
first describe the construction, which only uses classical
transversality techniques, of a symplectic cohomology group
on...
We will discuss a complete computation of Savelyev's
homomorphism associated to any coadjoint orbit of a compact Lie
group G, where the domain is restricted to the based loop homology
of G. This gives at the same time some applications to the...
We will discuss the existence of rational (multi)sections and
unirulings for projective families f:X→P1 with at most two singular
fibres. Specifically, we will discuss two ingredients for
constructing the above rational curves. The first is local...
In this talk, I will discuss recent joint work with D.
Cristofaro-Gardiner and B. Zhang showing that a generic
area-preserving diffeomorphism of a closed surface has a dense set
of periodic points. This follows from a result called a “smooth
closing...
This talk is based on a joint work with Thomas Kragh. Using the
generating function theory we split inject homotopy groups of
pseudo-isotopy and/or h-cobordism spaces into various spaces of
Legendrian manifolds, e.g. the space of Legendrian unknots...
In various areas of mathematics there exist "big fiber
theorems", these are theorems of the following type: "For any map
in a certain class, there exists a 'big' fiber", where the class of
maps and the notion of size changes from case to case.
Knots associated to overtwisted manifolds are less explored.
There are two types of knots in an overtwisted manifold – loose and
non-loose. Non-loose knots are knots with tight complements whereas
loose knots have overtwisted complements. While we...
