Geometric quantization via SYZ transforms

Weyl Quantization from Geometric Quantization

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Hamiltonian monodromy via geometric quantization and theta functions

In this paper, Hamiltonian monodromy is addressed from the point of view of geometric quantization, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections. In the case of completely integrable Hamiltonian systems with two degrees of freedom, a link is established between monodromy and (2-level) theta functions, by resorting to t...

Bounds On Some Geometric Transforms

A flip or edge-replacement can be considered as a transformation by which one edge e of a geometric figure is removed and an edge f (f 6= e) is inserted such that the resulting figure belongs to the same class as the original figure. This thesis is concerned with transformation of two kinds of geometric objects, namely, planar trees and planar paths, through the application of flips. A techniqu...

Doran–Harder–Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves

We prove the Doran–Harder–Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi– Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi–Yau manifold of X can be constructed by gluing the two mirror Landau– Ginzburg models of the quasi-Fano manifolds. The two crucial i...