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.