2006-09-15 and 2006-09-29

Tara Holm, Cornell University

Loop groups in symplectic geometry (I and II)

In the first lecture, I will begin with a discussion of Kac-Moody groups (over C). Homogeneous spaces of these arise in symplectic geometry. Focusing on the space of based loops in a compact connected Lie group, we will explore the symplectic geometry of these spaces. In the second lecture, I will discuss some joint projects with Harada, Henriques, Jeffrey and Mare. All necessary symplectic background will be reviewed.