Gromov-witten theory and mirror symmetry

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August undefined, 2024

WebA MIRROR THEOREM FOR GROMOV-WITTEN THEORY WITHOUT CONVEXITY JUN WANG Abstract. We prove a genus zero Givental-style mirror theorem for all complete … WebFor any nondegenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r -spin curves, which corresponds to the simple singularity A r − 1.

Hodge theoretic aspects of mirror symmetry - University of …

Webideas and methods from Gromov-Witten theory have led to both conjectures and theorems showing that the tautological part of the cohomology ring has a remarkable and profound structure. As an illustration, we describe a new approach to Faber’s intersection number ... approach to mirror symmetry. There is as of yet no ideal book introducing ... WebDec 24, 2007 · The Witten equation, mirror symmetry and quantum singularity theory Huijun Fan, Tyler J. Jarvis, Yongbin Ruan For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. paa or berry and associates

arXiv:math/0204168v1 [math.DG] 12 Apr 2002

WebOct 31, 2024 · A mirror theorem for Gromov-Witten theory without convexity. We prove a genus zero Givental-style mirror theorem for all complete intersections in proper toric … Webcohomological eld theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r-spin curves, which corresponds … Webto construct a canonical basis of functions on a cluster variety in terms of the log Gromov-Witten theory of the mirror cluster variety. Contents 1. Log geometry 1 2. Log and tropical Gromov-Witten theory 5 3. Cluster varieties 7 References 11 These are the notes for the author’s mini-course presented at the workshop \Valuations and bira- paa peterborough

Topics in Geometry: Mirror Symmetry - MIT …

[1807.02544] Localization and Mirror Symmetry - arXiv

WebFeb 2, 2024 · As a physicist, my understanding of mirror symmetry is very limited, and perhaps the most "mathematical" literature I have read on mirror symmetry is the book … WebJul 4, 2014 · The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes … paa of lexWebYau manifold is such a moduli space and they argue that the mirror symmetry duality is a Fourier-Mukai transformation. We review various aspects of the mirror symmetry conjecture and discuss a geometric ap-proach in proving it. The existence of rigid Calabi-Yau manifolds poses a serious challenge jennifer cook md tucson

"WebApr 13, 2024 · This is a sequel of our previous work. 35 35. Wang, Z. and Yang, C., “ Diagonal tau-functions of 2D Toda lattice hierarchy, connected (n, m)-point functions, and double Hurwitz numbers,” arXiv:2210.08712 (2024). In that paper, we have derived an explicit formula for connected (n, m)-point functions of diagonal tau-functions of the 2D … " - Gromov-witten theory and mirror symmetry

Gromov-witten theory and mirror symmetry

Mirror symmetry at higher genus - University of Pennsylvania

Websuperpotential written down by using the toric mirror map under a convergence assumption. This gives a method to compute open Gromov-Witten invariants using mirror … WebJan 10, 2016 · Realizing that mirror symmetry for Calabi–Yau manifolds is interpretable as an isomorphism of variations of Hodge structures, with the A-model, defined by the …

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Webin Gromov-Witten theory, or more generally, in topological string theory, the Laplace transform has an interpretation as mirror symmetry. More precisely, the A-model and B-model are two diﬀerent approaches to studying the geometry of Calabi-Yau manifolds in topological string theory. They are related through mir-ror symmetry.

WebThe mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain... Webpredictions of the mirror symmetry are veriﬁed for rational curves of all degrees. The results of Sections 9 – 11 can be immediately carried over to complete intersections ... The Gromov-Witten theory borrows from the quantum ﬁeld theory the name (quantum) correlators for numerical topological characteristics of the moduli spaces Xn,d ...

Webon “Homological Mirror Symmetry”, 2024. Video available at the:workshop’s website. ⋄ “Log geometric techniques for open invariants in mirror symmetry” at the Simons Center, 2016. Video available at:Stony-Brook video portal ⋄ “Log geometric techniques for open invariants in mirror symmetry”, at the IAS WebMIRROR SYMMETRY 203 directly from punctured invariants without the intervention of steps (1) and (2). ... of non-Archimedean Gromov-Witten theory should allow the …

WebAbstract: Large N duality relates open Gromov-Witten theory in the cotangent bundle of the 3-sphere to closed Gromov-Witten theory in the resolved conifold. We show how to …

WebThe origins of mirror symmetry; overview of the course 2 Deformations of complex structures 3 Deformations continued, Hodge theory; pseudoholomorphic curves, … jennifer cook orthopedics trinityWebHomological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). jennifer cook np shelby ncWebstance “superconformal ﬁeld theory” means that the theory depends only on the conformal structure on Σ rather than the Riemannian structure. There are vari ous ﬂavors of these theories, but the ones more relevant to mirror symmetry are the nonlinear sigma-models (the “target space”) is a Calabi-Yau manifold. Deﬁnition 1. paa officeWebMirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. jennifer cook md trinity flWebMirror symmetry was introduced in physics as a special duality between two N= 2 superconformal ﬁeld theories. Traditionally a N= 2 superconformal ﬁeld theory is constructed as a quantization of a non-linear σ-model with target a com-pact Calabi-Yau manifold equipped with a Ricci-ﬂat Kahler metric and a closed 2-form - the so called B … jennifer cook md cardiologyWeb2 In terms of this structure, describe the mirror to the quotient. Basic Answers (Torus case; 0th order approximation) 1 The mirror to a T-action on X is a holomorphic map X_!T_ C. 2 The mirror of X==T is the ber of X_over 1. Basic Answers (Compact, connected G; ( 1)st order approximation) 1 The mirror to a G-action on X is a holomorphic map ... jennifer cook wucfWebApr 4, 2024 · Abstract: Punctured Gromov-Witten theory of Abramovich-Chen-Gross-Siebert is an extension of logarithmic Gromov-Witten theory in which marked points … jennifer cook o\u0027toole