Triangulated categories play an important role in symplectic
topology. The aim of this talk is to explain how to combine
triangulated structures with persistence module theory in a
geometrically meaningful way. The guiding principle comes from
Let X be a compact symplectic manifold, and D a normal crossings
symplectic divisor in X. We give a criterion under which the
quantum cohomology of X is the cohomology of a natural deformation
of the symplectic cochain complex of X \ D. The...
Viterbo conjectured that a normalized symplectic capacity, on
convex domains of a given volume, is maximized for the ball. A
stronger version of this conjecture asserts that all normalized
symplectic capacities agree on convex domains. Since...
I will start by explaining Takahashi's homological mirror
symmetry (HMS) conjecture regarding invertible polynomials, which
is an open string reinterpretation of Berglund-Hubsch-Henningson
mirror symmetry. In joint work with A. Polishchuk, we...
The Arnold conjecture about fixed points of Hamiltonian
diffeomorphisms was partly motivated by the celebrated
Poincare-Birkhoff fixed point theorem for an area-preserving
homeomorphism of an annulus in the plane. Despite the fact that the
This talk reports on joint work with Maria Bertozzi, Tara Holm,
Emily Maw, Grace Mwakyoma, Ana Rita Pires, and Morgan Weiler on a
WiSCon project to investigate the embedding capacity function of
the one-point blow up of ?P2. We found three new...
This talk will discuss a new algebraic structure called
triangulated persistence category (TPC). It combines the
triangulated category structure with the persistence module
structure. This algebraic structure can be used to associate a
For a weighted homogeneous polynomial and a choice of a diagonal
symmetry group, we define a new Fukaya category based on wrapped
Fukaya category of its Milnor fiber together with monodromy
information. It is analogous to the variation operator in...
In a joint work with Pierre Dehornoy and Ana Rechtman, we prove
that on a closed 3-manifold, every nondegenerate Reeb vector field
is supported by a broken book decomposition. From this property, we
deduce that in dimension 3 every nondegenerate...
In a joint work with Laurent Côté we show the
following result. Any Lagrangian plane in the cotangent bundle of
an open Riemann surface which coincides with a cotangent fibre
outside of some compact subset, is compactly supported