Joint Colloquium: Sawon -- Holomorphic coisotropic reduction

THE UNIVERSITIES OF SYDNEY AND NEW SOUTH WALES

          SCHOOLS OF MATHEMATICS AND STATISTICS


___________________JOINT COLLOQUIUM______________________


Speaker: Prof. Justin Sawon (Colorado State University)
    
Title:   Holomorphic coisotropic reduction.

Date:    Tuesday, 14 July 2009
Time:    12:00 noon
Venue:   Room 173 Carslaw Building

Abstract:

Coisotropic reduction can be regarded as a generalization 
of symplectic reduction. Given a symplectic manifold X of 
dimension 2n with symplectic form $\omega$, a submanifold 
Y of dimension at least n is coisotropic if $\omega|_Y$ 
has the smallest possible rank at every point of Y. The 
null directions of $\omega|_Y$ then induce a foliation 
F on Y and the space of leaves Y/F is a symplectic 
manifold of lower dimension.

In this talk we will consider coisotropic reduction in 
holomorphic symplectic geometry. The main difficulty is 
ensuring that the leaves of the foliation are compact, 
so that Y/F is well-defined. We will describe some 
examples and applications of holomorphic coisotropic 
reduction.