1. CJM 2013 (vol 66 pp. 31)
 Bailey, Michael

Symplectic Foliations and Generalized Complex Structures
We answer the natural question: when is a transversely holomorphic
symplectic foliation induced by a generalized complex structure? The
leafwise symplectic form and transverse complex structure determine an
obstruction class in a certain cohomology, which vanishes if and only
if our question has an affirmative answer. We first study a component
of this obstruction, which gives the condition that the leafwise
cohomology class of the symplectic form must be transversely
pluriharmonic. As a consequence, under certain topological
hypotheses, we infer that we actually have a symplectic fibre bundle
over a complex base. We then show how to compute the full obstruction
via a spectral sequence. We give various concrete necessary and
sufficient conditions for the vanishing of the obstruction.
Throughout, we give examples to test the sharpness of these
conditions, including a symplectic fibre bundle over a complex base
which does not come from a generalized complex structure, and a
regular generalized complex structure which is very unlike a
symplectic fibre bundle, i.e., for which nearby leaves are not
symplectomorphic.
Keywords:differential geometry, symplectic geometry, mathematical physics Category:53D18 

2. CJM 2012 (vol 65 pp. 1164)
 Vitagliano, Luca

Partial Differential Hamiltonian Systems
We define partial differential (PD in the following), i.e., field
theoretic analogues of Hamiltonian systems on abstract symplectic
manifolds and study their main properties, namely, PD Hamilton
equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in
standard multisymplectic approach to Hamiltonian field theory, in our
formalism, the geometric structure (kinematics) and the dynamical
information on the ``phase space''
appear as just different components of one single geometric object.
Keywords:field theory, fiber bundles, multisymplectic geometry, Hamiltonian systems Categories:70S05, 70S10, 53C80 
