Geometry Seminar


Theta Functions on the Kodaira ─ Thurston Manifold


Dr. William Kirwin

Max Plank Institut für Mathematik




The Kodaira-Thurston manifold M, a symplectic, nonKaehler 4-manifold, is a nontrivial 2-torus bundle over the 2-torus.  We will discuss how the classical theory of theta functions, usually associated to complex tori, can be extended to M.  Our constructions, though, do not seem to be unique to M and are likely applicable in more generality. There is a 5 dimensional Lie group G associated to M which plays a role analogous to that of the Heisenberg group in the classical theory.  We essentially use Kirillov's orbit method to describe the unitary representations of G, which are then used to construct theta functions associated to M.  Somewhat surprising is that the symplectic geometry of M is reflected by the representation theory of G; in particular, Lagrangian and special Lagrangian foliations and fibrations of M arise as algebraic objects in the orbit method analysis. (This is joint work with Alejandro Uribe.)




February 13, 2008 (Wednesday)


2:45 – 3:45pm


Room 517, Meng Wah Complex, HKU




All are welcome