In this talk I will introduce barcode entropy and discuss its
connections to topological entropy. The barcode entropy is a
Floer-theoretic invariant of a compactly supported Hamiltonian
diffeomorphism, measuring, roughly speaking, the exponential...
I will start by explaining the construction of a formal scheme
starting with an integral affine manifold Q equipped with a
decomposition into Delzant polytopes. This is a weaker and more
elementary version of degenerations of abelian varieties...
In this talk I will discuss a joint project with Yuanpu Liang in
which we establish several properties of the sequence of symplectic
capacities defined by Gutt and Hutchings for star-shaped domains
using S1-equivariant symplectic homology. Among the...
In this short talk, I will introduce the notion of n-morphisms
between two A-infinity algebras. These higher morphisms are such
that 0-morphisms correspond to standard A-infinity morphisms and
1-morphisms correspond to A-infinity homotopies. Their...
A generalization of the cartesian product and the free sum of
two convex domains is the p-product operation. We investigate the
behavior of symplectic capacities with respect to symplectic
p-products, and we give applications related to Viterbo's...
In this talk, I will present two results relating the
qualitative dynamics of non-degenerate Hamiltonian isotopies on
surfaces to the structure of their Floer complexes.
The first will be a topological characterization of those Floer
chains...
A compact four dimensional completely integrable system f:M→R2
is semitoric if it has only non-degenerate singularities, without
hyperbolic blocks, and one of the components of generates a circle
action. Semitoric systems have been extensively...
I will discuss some quantitative aspects for Legendrians in a
(more or less) general contact manifold. These include lower bounds
on the number of Reeb chords between a Legendrian and its contact
Hamiltonian image, the non-degeneracy of the Chekanov...
In this talk we introduce a type of surgery decomposition of
Weinstein manifolds we call simplicial decompositions. We will
discuss the result that the Chekanov-Eliashberg dg-algebra of the
attaching spheres of a Weinstein manifold satisfies a...
The notion of positive (non-negative) contact isotopy, defined
by Eliashberg and Polterovich, leads to two relations on the group
of contactomorphisms. These relations resemble the causal relations
of a Lorentzian manifold. In this talk we will...
