# Jerusalem Mathematics Colloquium

Thursday, 13th March 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Patrick Iglesias-Zemmour

(HU)

"Moment Maps"

** Abstract: **In the 19th century, Emmy Noether was the
first to relate invariance, in a dynamical system, with constants of
motions. The modern version of this theorem, with the coming of
symplectic formalism in classical (or quantum) mechanics, involves
the so-called Moment Map. This moment map is associated to every
symplectic or pre-symplectic manifold together with an invariant
action of a Lie group. It is defined on the manifold with values in
the dual of the Lie algebra of the group of symmetries. Souriau's
version of Noether's theorem states that: the moment map is constant
on the characteristics of the pre-symplectic form. But the role of
this moment map has increased in parallel with the development of
symplectic geometry, it became the fundamental tool for
classification theorems in symplectic geometry, in presence of
symmetries. The classical version of the moment map is now well
established, since the beginning of the 70's. But in the recent
decades, some objects looking like moment maps appeared in other
contexts, not covered by the classical formalism: spaces regarded as
singular in the classical framework of differential geometry,
orbifolds, quotients by symplectic reductions, infinite dimensional
modular spaces etc. It was interesting to try to give to these many
recent heuristic examples and constructions a unique simple and
efficient framework.

Light refreshments will be served in
the faculty lounge at 3:30.

List of talks, 2007-08

Archive of talks