The existence of rational plane curves of a given degree with
prescribed singularities is a subtle and active area in algebraic
geometry. This problem turns out to be closely related to difficult
enumerative problems which arise in symplectic field...
I will talk about an ongoing project that explores the
construction of high dimensional Legendrian spheres from supporting
open books and contact structures. The input is a Lagrangian disk
filling of a Legendrian knot in the binding. We try to...
I will explain the construction of a new class of Liouville
domains that live in a complex torus of arbitrary dimension, whose
boundary dynamics encodes information about the singularities of a
toric compactification. The primary motivation for this...
In this talk, we will study the Floer Homology barcodes from a
dynamical point of view. Our motivation comes from recent results
in symplectic topology using barcodes to obtain dynamical results.
We will give the ideas of new constructions of...
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...
