A continuous representation of a profinite group induces a
continuous pseudorepresentation, where a pseudorepresentation is
the data of the
characteristic polynomial coefficients. We discuss the geometry of
the resulting map from the moduli formal...
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...
The theorem of the title is that if the L-function L(E,s) of an
elliptic curve E over the rationals vanishes to order r=0 or 1 at
s=1 then the rank of the group of rational rational points of E
equals r and the Tate-Shafarevich group of E is finite...
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...
A few years ago Ichino-Ikeda formulated a quantitative version
of the Gross-Prasad conjecture, modeled after the classical work of
Waldspurger. This is a powerful local-to-global principle which is
very suitable for analytic and arithmetic...
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...
The trace formula has been the most powerful and mainstream tool
in automorphic forms for proving instances of Langlands
functoriality, including character relations. Its generalization,
the relative trace formula, has also been used to prove...
We will present joint work with Will Merry. Using spectral
invariants in Rabinowitz Floer homology we present an abstract
contact non-squeezing theorem for periodic contact manifolds. We
then exemplify this in concrete examples. Finally we explain...
