ERA

Download the full-sized PDF of Topological Recursion and Genus One Quantum Curves: An Accessible ExplorationDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R3RN30K9B

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

Topological Recursion and Genus One Quantum Curves: An Accessible Exploration Open Access

Descriptions

Other title
Subject/Keyword
topological recursion
elliptic
modular
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Dauphinee, Tyler LJ
Supervisor and department
Bouchard, Vincent (Mathematical and Statistical Sciences)
Examining committee member and department
Favero, David (Mathematical and Statistical Sciences)
Creutzig, Thomas (Mathematical and Statistical Sciences)
Marsiglio, Frank (Physics)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Physics
Date accepted
2017-01-20T10:32:47Z
Graduation date
2017-06:Spring 2017
Degree
Master of Science
Degree level
Master's
Abstract
We explore the connection between Eynard-Orantin Topological Recursion (EOTR) and the asymptotic solutions to differential equations constructed with the WKB method (named for its creators Wentzel, Kramers and Brillouin). Using the Airy spectral curve as an initial example, we propose a general connection between topological recursion and WKB solutions to the quantum curve generated via quantization of the defining algebraic curve. We proceed further by examining the proposed connection in the context of the genus one family of Weierstrass spectral curves. We construct the perturbative wave-function and show that it is annihilated by a differential operator which is not a quantization of the spectral curve. Furthermore, as a consequence of equivalent approaches we also obtain an infinite collection of identities relating cycle integrals of elliptic functions to quasi-modular forms.
Language
English
DOI
doi:10.7939/R3RN30K9B
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2017-01-20T17:32:48.345+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 480165
Last modified: 2017:06:13 12:24:42-06:00
Filename: Dauphinee_Tyler_LJ_201701_MSc.pdf
Original checksum: 820b37323de97b64b0ea8671125cecc7
Well formed: true
Valid: true
File title: Introduction
File title: Topological Recursion and Genus One Quantum Curves: An Accessible Exploration
File author: Tyler Dauphinee
Page count: 95
Activity of users you follow
User Activity Date