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.