I will review two combinatorial constructions of integrable
systems: Goncharov-Kenyon construction based on counting perfect
matchings in bipartite graphs, and
Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on
counting paths in networks...
In a work with Jacques Fejoz, we consider the conformal dynamics
on a symplectic manifold , i.e. for which the symplectic form is
transformed colinearly to itself. In the non-symplectic case, we
study the problem of isotropy and uniqueness of...
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...
