Lectures on symplectic, Kahler and hyper-Kahler geometry
3:00pm-5:00pm
Weiqiang He (Sun Yat-sen University)
Lecture 1: Symplectic geometry
In this lecture, we will introduce the basic aspects of symplectic geometry, including sympletic form, Hamiltonian vector field, moment map, symplectic quotient etc. We will also discuss some basic examples of symplectic manifold.
Lecture 2: Kahler geometry and hyperkahler geometry
This lecture is a quick review of the related topic of Kahler and hyperkahler geometry, including Hermitian metric, Kahler and hyperkahler structure, Kahler and hyperkahler quotient.
Lecture 3: Nahm equation and hyperkahler structure
In this lecture, we will discuss an important example of hyperkahler manifold: the space of solutions of Nahm equation with certain boundary condition. We will discuss the relation between this space and the coadjoint orbit of simple Lie algebra, and the hyperkahler structure on it.