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On Gromov-Witten Invariants, Hurwitz Numbers and Topological Recursion Open Access


Other title
Topological Recursion
Gromov-Witten Invariants
Hurwitz Numbers
Mathematical Physics
Type of item
Degree grantor
University of Alberta
Author or creator
Anajao, Rosa P
Supervisor and department
Bouchard, Vincent
Examining committee member and department
Vincent Bouchard
Eric Woolgar
Jochen Kuttler
Department of Mathematical and Statistical Sciences
Thomas Creutzig
Department of Mathematical and Statistical Sciences
Mathematical Physics
Date accepted
Graduation date
Master of Science
Degree level
In this thesis, we present expositions of Gromov-Witten invariants, Hurwitz numbers, topological recursion and their connections. By remodeling theory, open Gromov-Witten invariants of C^3 and C^3/Z_a satisfy the topological recursion of Eynard-Orantin defined on framed mirror curve of toric Calabi-Yau three orbifold target spaces. Studies show that simple/orbifold Hurwitz numbers can be obtained using topological recursion with spectral curve given by Lambert/a-Lambert curve. Also, both the open Gromov-Witten invariants of toric Calabi-Yau three orbifold and the simple and double Hurwitz numbers can be formulated via Hodge integrals. We extend these connections by determining the relationship between the open Gromov-Witten invariants of C^3/Z_a (with insertions of orbifold cohomology classes) and the full double Hurwitz numbers through referring to their Hodge integral formulations and to orbifold Riemann-Roch formula. By remodeling theory and mirror theorem for disk potentials, we make a conjecture relating a specific type of double Hurwitz numbers H_g(ν(γ, 2), μ) and topological recursion. We predict that these double Hurwitz numbers H_g(ν(γ, 2), μ) can be generated using topological recursion defined on the spectral curve ye^{−2y} − τxe^{−y} + x^2 = 0.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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