Maher, Rob (2024). Predictions in open Fan-Jarvis-Ruan-Witten theory via mirror symmetry, modularity and wall-crossing. University of Birmingham. Ph.D.
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Maher2024PhD.pdf
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Abstract
In recent works of Buryak, Clader, Gross, Kelly and Tessler, genus zero open enumerative theories and their mirrors for the Landau-Ginzburg models W_0 = x^r and W_0 = x^r + y^s were constructed. We build on this work by defining an open mirror B-model with gravitational descendants for any Fermat, chain or loop polynomial. This is done by presenting a recursive algorithm for finding flat coordinates of Dubrovin’s Frobenius manifold for a Landau-Ginzburg B-model. Furthermore, we present formulas for these coordinates for any ADE or elliptic singularity. Although these open Saito potentials do not yet have an enumerative interpretation, we present explicit formulas for these generating functions, together with modularity properties in the elliptic case. Finally, we find that the B-model exhibits a wall-crossing structure. We classify this structure by describing a Lie group action of wall-crossing transformations, which we prove is faithful and transitive in the rank two case.
| Type of Work: | Thesis (Doctorates > Ph.D.) | |||||||||
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| Award Type: | Doctorates > Ph.D. | |||||||||
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| Licence: | All rights reserved | |||||||||
| College/Faculty: | Colleges > College of Engineering & Physical Sciences | |||||||||
| School or Department: | School of Mathematics | |||||||||
| Funders: | Engineering and Physical Sciences Research Council | |||||||||
| Subjects: | Q Science > QA Mathematics | |||||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/15556 |
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