In this talk, we first introduce the notion of a continuous
cover of a manifold parametrised by any compact manifold
endowed with a mass 1 volume-form. We prove that any such cover
admits a partition of unity where the usual sum is replaced
by...
We present a full $h$-principle (relative, parametric,
$C^0$-close) for the simplification of singularities of Lagrangian
and Legendrian fronts. More precisely, we prove that if there is no
homotopy theoretic obstruction to simplifying the...
I hope to talk more about how to find generators for Fukaya
categories using symplectic version of the minimal model program in
examples such as symplectic quotients of products of spheres and
moduli spaces of parabolic bundles.
Symplectic homology for a Liouville cobordism (possibly filled at
the negative end) generalizes simultaneously the symplectic
homology of Liouville domains and the Rabinowitz-Floer homology of
their boundaries. I intend to explain a conceptual...
$C^r$ closing lemma is an important statement in the theory of
dynamical systems, which implies that for a $C^r$ generic system
the union of periodic orbits is dense in the nonwondering domain.
$C^1$ closing lemma is proved in many classes of...
The standard WDVV equations are PDEs in the potential function that
generates Gromov-Witten invariants. These equations imply relations
on the invariants, and sometimes allow computations thereof, as
demonstrated by Kontsevich-Manin (1994). We prove...
After introducing Hamiltonian homeomorphisms and recalling some of
their properties, I will focus on fixed point theory for this class
of homeomorphisms. The main goal of this talk is to present the
outlines of a $C^0$ counterexample to the Arnold...
I will recall the construction of the space of states in a gauged
topological A-model. Conjecturally, this gives the quantum
cohomology of Fano symplectic quotients: in the toric case, this is
Batyrev’s presentation of quantum cohomology of toric...
Let $n > 1$. Given two maps of an $n$-dimensional sphere into
Euclidean $2n$-space with disjoint images, there is a $\mathbb Z/2$
valued linking number given by the homotopy class of the
corresponding Gauss map. We prove, under some restrictions on...
