We define a quantum product on the cohomology of a symplectic
manifold relative to a Lagrangian submanifold, with coefficients in
a Novikov ring. The associativity of this product is equivalent to
an open version of the WDVV equations for an...
In all known explicit computations on Weinstein manifolds, the
self-wrapped Floer homology of non-compact exact Lagrangian is
always either infinite-dimensional or zero. We will explain why a
global variant of this observed phenomenon holds in broad...
Inspired by the symplectic Banach-Mazur distance, proposed by
Ostrover and Polterovich in the setting of non-degenerate
starshaped domains of Liouville manifolds, we define a distance on
the space of contact forms supporting a given contact...
In 1985, Casson introduced an invariant of integer homology
3-spheres by counting SU(2)SU(2)-representations of the
fundamental groups. The generalization of Casson invariant by
considering Lie groups SU(n) has been long expected, but the
original...
We study configurations of disjoint Lagrangian submanifolds in
certain low-dimensional symplectic manifolds from the perspective
of the geometry of Hamiltonian maps. We detect infinite-dimensional
flats in the Hamiltonian group of the two-sphere...
A classical construction in topology associates to a space X and
prime p, a new "localized" space Xp whose homotopy and homology
groups are obtained from those of X by inverting p. In this talk, I
will discuss a symplectic analog of this...
The group of Hamiltonian diffeomorphisms of a symplectic
manifold admits a remarkable bi-invariant metric, called Hofer’s
metric. My talk will be about a recent joint work with Dan
Cristofaro-Gardiner and Vincent Humilière resolving the
following...
I will explain the notion of twisted generating function and
show that a closed exact Lagrangian submanifold LL in the
cotangent bundle of MM admits such a thing. The type of
function arising in our construction is related to Waldhausen's
tube space...
Gross and Siebert have recently proposed an "intrinsic"
programme for studying mirror symmetry. In this talk, we will
discuss a symplectic interpretation of some of their ideas in the
setting of affine log Calabi-Yau varieties. Namely, we
describe...
