The Conley conjecture, recently established by Nancy Hingston,
asserts that every Hamiltonian diffeomorphism of a standard
symplectic 2n-torus admits infinitely many periodic points. While
this conjecture has been extended to more general closed...
This is a series of 3 talks on the topology of Stein manifolds,
based on work of Eliashberg since the early 1990ies. More
specifically, I wish to explain to what extent Stein structures are
flexible, i.e. obey an h-principle. After providing some...
The Arnold conjecture in Symplectic Topology states existence of
many fixed points for Hamiltonian symplectomorphisms of a compact
symplectic manifold. In my talk I will discuss an analogue of this
conjecture in Contact Topology, based on the notion...
We study particular solutions of the "inner equation" associated
to the splitting of separatrices on "generalized standard maps". An
exponentially small complete expression for their difference is
obtained. We also provide numerical evidence that...
We review some recent developments in KAM theory. By exploiting
some identities of a geometric nature, one can obtain iterative
steps which lead to numerical algorithms and which can follow the
tori till breakdown. We present theoretical results in...
We present a Hamiltonian framework for higher-dimensional vortex
filaments (or membranes) and vortex sheets as singular 2-forms with
support of codimensions 2 and 1, respectively, i.e. singular
elements of the dual to the Lie algebra of divergence...
There are indications that in the 80s Guillemin posed a
question: If billiard maps are conjugate, can we say that domains
are the same up to isometry? On one side, we show that conjugacy of
different domains can't be C^1 near the boundary. In...
