Use this URL to cite or link to this record in EThOS:
Title: Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting
Author: Bousseau, Pierrick
ISNI:       0000 0004 7655 5272
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 2018
Availability of Full Text:
Access from EThOS:
Access from Institution:
We present three results, at the intersection of tropical geometry, enumerative geometry, mirror symmetry and non-commutative algebra. 1. A correspondence between Block-Göttsche q-refined tropical curve counting and higher genus log Gromov-Witten theory of toric surfaces. 2. A correspondence between q-refined two-dimensional Kontsevich-Soibelman scattering diagrams and higher genus log Gromov-Witten theory of log Calabi-Yau surfaces. 3. A q-deformation of the Gross-Hacking-Keel mirror construction, producing a deformation quantization with canonical basis for the Gross-Hacking-Keel families of log Calabi-Yau surfaces. These results are logically dependent: the proof of the third result relies on the second, whose proof itself relies on the first. Nevertheless, each of them is of independent interest.
Supervisor: Thomas, Richard Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral