location: at the Institut de Mathématique d’Orsay, bldg 307
(directions: https://www.imo.universite-paris-saclay.fr/en/contact/)
10h45 Joan Licata (Australian National University)
Heegaard splittings and the tight Giroux Correspondence
Room 3L15 - Exceptional symplectic and contact geometry seminar
Abstract:
The Giroux Correspondence famously characterises the open books
supporting a fixed isotopy class of contact structures. In this talk
I’ll sketch a new proof of the Giroux Correspondence for tight contact
three-manifolds. Our approach relies on convex surface theory and the
close relationship between open books and Heegaard splittings. This is
joint work with V Vertesi.
14h Patricia Dietzsch (ETH Zurich)
Lagrangian Hofer metric and barcodes
Room 2L8 - Weekly seminar of the team of Topology and Dynamics at LMO
Abstract: A
major tool in symplectic topology to study Lagrangian submanifolds are
Lagrangian Floer homology groups. A richer algebraic invariant can be
obtained using filtered Lagrangian Floer theory. The resulting object is
a persistence module, giving rise to a barcode, whose bar lengths are
invariants for pairs of Lagrangians. It is well-known that these numbers
are lower bounds of the Lagrangian Hofer distance between the two
Lagrangians.
In
this talk we will discuss a reverse inequality: We will show an upper
bound of the Lagrangian Hofer distance between equators in the cylinder
in terms of a weighted sum of the lengths of the finite bars and the
spectral distance.
15h45 Guillem Cazassus (University of Oxford)
Hamiltonian actions on Fukaya categories
Room 2L8 - Exceptional symplectic and contact geometry seminar
Abstract: We
will talk about algebraic structures arising in Lagrangian Floer
homology in the presence of a Hamiltonian action of a compact Lie group.
First, we will show how the Lagrangian Floer complex can be equipped
with an A-infinity module structure over the Morse complex of the group,
and how this action permits to define equivariant versions of Floer
homology. We will then explain how this structure interacts with the
structure of the Fukaya category: both can be packaged into (our version
of) an A-infinity bialgebra action, giving an alternative answer to a
conjecture of Teleman. This should enable one to build an extended
topological field theory corresponding to Donaldson-Floer theory. This
is based on two joint work in progress, one with Paul Kirk, Mike
Miller-Eismeier and Wai-Kit Yeung, and another with Alex Hock and
Thibaut Mazuir.
