Mark Hamilton, Mount Allison University
Toric degenerations and independence of polarization
In the theory of geometric quantization, one essential ingredient is the choice of a "polarization"; a natural question is then whether the resulting quantization depends on this choice. One recent approach to the question of "independence of polarization" is using a deformation of complex structure to "deform" one polarization into another. Originally applied to smooth toric varieties, this has also been applied to a broader class of examples, such as flag varieties, by using a toric degeneration.
In this talk I will present an overview of this program (including a short introduction to the key ideas of geometric quantization), and mention several examples of its application, including flag manifolds, more general varieties, and moduli spaces of flat connections (work in progress).
MC 5403