I will discuss how the Deligne-Mumford compactification of
curves arises from the uncompactified moduli spaces of curves as a
result of some algebraic operations related to (pr)operadic
structures on the moduli spaces. I will describe how a...
We present recent developments in symplectic geometry and
explain how they motivated new results in the study of cluster
algebras. First, we introduce a geometric problem: the study of
Lagrangian surfaces in the standard symplectic 4-ball
bounding...
Persistence modules and barcodes are used in symplectic topology
to define new invariants of Hamiltonian diffeomorphisms, however
methods that explicitly calculate these barcodes are often unclear.
In this talk I will define one such invariant...
The ellipsoidal embedding function of a symplectic four manifold
M measures how much the symplectic form on M must be dilated in
order for it to admit an embedded ellipsoid of some eccentricity.
It generalizes the Gromov width and ball packing...
The spectral norm provides a lower bound to the Hofer norm. It
is thus natural to ask whether the diameter of the spectral norm is
finite or not. During this short talk, I will give a sketch of the
proof that, in the case of Liouville domains, the...
I will explain how to construct the Ruelle invariant of a
symplectic cocycle over an arbitrary measure preserving flow. I
will provide examples and computations in the case of Hamiltonian
flows and Reeb flows (in particular, for toric domains). As...
Relative symplectic cohomology is a Floer theoretic invariant
associated with compact subsets K of a closed or geometrically
bounded symplectic manifold M. The motivation for studying it is
that it is often possible to reduce the study of global...
Gromov-Witten invariants for a general target are
rational-valued but not necessarily integer-valued. This is due to
the contribution of curves with nontrivial automorphism groups. In
1997 Fukaya and Ono proposed a new method in symplectic
geometry...
Homeomorphism is called contact if it can be written as C0-limit
of contactomorphisms. The contact version of Eliashberg-Gromov
rigidity theorem states that smooth contact homeomorphisms preserve
contact structure. Submanifold L of a contact...
