2008-10-24

Joshua Bowman, Cornell University

Some Variational and Asymptotic Methods in the Study of Complex Structures

This lecture has two main goals. The first is to give some insights into the geometry of the classical Siegel half-plane and a natural boundary it has. The second is to use these results to answer a question of J. Hubbard regarding certain families of complex structures on the odd cohomology of a surface. We will show that geodesics in the Siegel half-plane are easily understood in terms of isotropic subspaces of a symplectic vector space.