Theta
Functions on the Kodaira ─ Thurston Manifold
Dr. William Kirwin
Max Plank Institut für Mathematik
Abstract
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.)
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Date: |
February 13, 2008 (Wednesday) |
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Time: |
2:45 – 3:45pm |
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Place: |
Room 517, Meng Wah Complex, HKU |
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All are
welcome |
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