To apply the technique of virtual fundamental cycle (chain) in
the study of pseudo-holomorphic curve, we need to construct certain
structure, which we call Kuranishi strucuture, on its moduli space.
In this talk I want to review certain points of...
This is joint work with A. B. Goncharov. To any convex integer
polygon we associate a Poisson variety, which is essentially the
moduli space of connections on line bundles on (certain) bipartite
graphs on a torus. There is an underlying integrable...
Fix a metric (Riemannian or Finsler) on a compact manifold M.
The critical points of the length function on the free loop space
LM of M are the closed geodesics on M. Filtration by the length
function gives a link between the geometry of closed...
In 1985 Misha Gromov proved his Nonsqueezing Theorem, and hence
constructed the first symplectic 1-capacity. In 1989 Helmut Hofer
asked whether symplectic d-capacities exist if 1 d n. I will
discuss the answer to this question and its relevance in...
