The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning

Abstract

We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student and using Calabi-Yau spaces as an exciting play-ground, we intend to teach some mathematics to the budding physicist, some physics to the budding mathematician, and some machine-learning to both. Based on various lecture series, colloquia and seminars given by the author in the past year, this writing is a very preliminary draft of a book to appear with Springer, by whose kind permission we post to ArXiv for comments and suggestions.

book to appear with Springer; v1 #pages = #irreps(Monster), 44 figures; v2 substantially expanded: about 100 extra pages and 10 figures added

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• Brane Tilings
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• Neural Networks and Quantum Field Theory
• An algorithm for the classification of smooth Fano polytopes
• Moduli of representations of quivers
• AdS/CFT as a deep Boltzmann machine
• Supersymmetry versus Gauge Symmetry on the Heterotic Landscape
• Calabi-Yau threefolds with large h^{2, 1}
• Deep Learning the Hyperbolic Volume of a Knot
• Holography as deep learning
• Deep Learning for Symbolic Mathematics
• Brane Tilings and Specular Duality
• Getting CICY High
• Classifying Calabi-Yau threefolds using infinite distance limits
• Quiver Mutations, Seiberg Duality and Machine Learning
• On moduli spaces of quiver representations associated with dimer models
• Distinguishing Elliptic Fibrations with AI
• Is Deep Learning a Renormalization Group Flow?
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• Calabi-Yau Manifolds with Large Volume Vacua
• Universal Approximation with Deep Narrow Networks
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• Deep learning and k-means clustering in heterotic string vacua with line bundles
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Cited by in corpus (28)

• Machine learning Calabi-Yau metrics
• Getting CICY High
• Quiver Mutations, Seiberg Duality and Machine Learning
• Machine Learning Calabi-Yau Four-folds
• Distinguishing Elliptic Fibrations with AI
• Machine Learning Lie Structures & Applications to Physics
• Hilbert Series, Machine Learning, and Applications to Physics
• Neurons on Amoebae
• Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer
• Machine-Learning Arithmetic Curves
• Machine-Learning Number Fields
• Lectures on the Calabi-Yau Landscape
• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
• Cluster Algebras: Network Science and Machine Learning
• Deep learning complete intersection Calabi-Yau manifolds
• Universes as Big Data
• Dynamics of genetic code evolution: The emergence of universality
• Mahler Measure for a Quiver Symphony
• Machine-learning a virus assembly fitness landscape
• Lectures on Naturalness, String Landscape and Multiverse
• Congruences on K-theoretic Gromov--Witten invariants
• Machine-Learning the Classification of Spacetimes
• Calabi-Yau threefolds in ${\mathbb{P}}^n$ and Gorenstein rings
• Poisson structures on the conifold and local Calabi-Yau threefolds
• Hodge-Gromov-Witten theory
• Self-regularizing restricted Boltzmann machines
• Measuring global properties of neural generative model outputs via generating mathematical objects
• Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory