Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 38 for “"Mirror symmetry"”.
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On Berglund-Hübsch-Krawitz Mirror Symmetry
… that have Berglund-Hübsch-Krawitz (BHK) mirrors. These Calabi-Yau orbifolds are certain finite symplectic quotients of hypersurfaces in weighted-projective space. First, we will describe their birational geometry using Shioda maps and prove that so-called alternate mirrors are birational. …
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Toric mirror symmetry and GIT windows
… based on the author's joint work [HZ20], studies mirror symmetry for toric varieties from the perspective of geometric invariant theory. We translate GIT constructions of toric varieties into skeletal terms and study them in the context of wrapped Fukaya categories and wrapped constructible …
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Gauged Linear Sigma Model and Mirror Symmetry
… study of gauged linear sigma models (GLSMs) and mirror symmetry. The first chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying supersymmetric localization. The …
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Mirrors to Toric Degenerations via Intrinsic Mirror Symmetry
We explore the connection between two mirror constructions in Gross-Siebert mirror symmetry: toric degeneration mirror symmetry and intrinsic mirror symmetry. After briefly exploring the case of degenerations of elliptic curves, we show that the Gross-Siebert mirror construction for minimal …
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Homological mirror symmetry for a Calabi-Yau hypersurface in projective space
… is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the …
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Mirror symmetry and the K theory of a p-adic group
… correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth </= e "truncated" analogue …
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Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces
… of Calabi-Yau varieties in the context of mirror symmetry from a singular affine structure with additional data. We will show that the two instanton correction problems are equivalent in an appropriate sense via the identification of the wall crossing formulas in the metric problem with …
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Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations
… of the 2D fibers, we then study the mirror symmetry structure of elliptic toric hypersurface Calabi-Yau threefolds. We show that the mirror symmetry of Calabi-Yau manifolds factorizes between the toric fiber and the base: if there exist 2D mirror fibers of a pair of mirror reflexive …
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Boundaries, States and Cohomology in Three-Dimensional N = 4 Theories
… classes are further shown to be exchanged under mirror symmetry, via collision with a mirror symmetry interface. By computing boundary amplitudes, the enriched Neumann boundary conditions reproduce the elliptic stable envelopes of Aganagic-Okounkov, and the mirror symmetry interface the mother …
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A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations
… of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.
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Dualities and Categorical Structures from 2D Up
… specifically, holographic duality, homological mirror symmetry, and 3D mirror symmetry. As we shall see, the common ground in between the two paths taken in this treatment is the role played by amplitutdes in studying fundamental interactions and the properties of the vacuum structure, as well …
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Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
… lay the groundwork for verifying predictions of mirror symmetry for the real quintic.
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Supersymmetric Backgrounds in string theory
… of Grassmannians. In the next part, we consider mirror symmetry for certain gauge theories with gauge groups $F_4$, $E_6$, and $E_7$. In the last part of this thesis, we study whether certain branched-double-cover constructions in Landau-Ginzburg models can be extended to higher covers.
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Equivariant quantum cohomology and the geometric Satake equivalence
Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a …
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D-branes on Calabi-Yau Spaces
… of these moduli and serves, together with mirror symmetry, as a tool to compare the two descriptions. We give an extensive and general presentation of these two descriptions for the class of Fermat hypersurfaces in weighted projective spaces. We explicitly carry out the comparison in many …
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Multiplicative Global Springer Theory
… central to many thriving research areas, such as mirror symmetry, non-abelian Hodge theory and the geometric Langlands program. They are also useful for globalizing representation-theoretic phenomena such as Springer theory and the study of Springer fibers. In the local and global settings, …
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve
… Lagrangian submanifolds in the Landau-Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the twisting sheaf 0(1), and hence their Floer cohomology groups form an algebra isomorphic …
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Flux compactifications of Type II string theories under non-perturbative dualities
… the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the generalisation of T duality to include Calabi-Yaus, mirror symmetry. The requirement of the effective theory superpotential being invariant under these …
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Birational Invariance of Punctured Log Gromov-Witten Theory and Intrinsic Mirror Constructions
… Gromov-Witten theory and their application to mirror symmetry. We first prove for log Calabi-Yau varieties satisfying a semi-positivity assumption that the Gross-Siebert logarithmic mirror construction encodes solutions to enumerative problems considered in the non-archimedean construction of …
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Symplectic properties of Milnor fibres
… cycles. Also, this allows progress towards mirror symmetry for unimodal singularities, which are one level of complexity up from the simple ones.
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