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

TL;DR

This paper introduces Calabi-Yau manifolds through an interdisciplinary approach, combining geometry, physics, and machine learning, aimed at beginners to foster understanding across these fields.

Contribution

It provides a pedagogical overview connecting Calabi-Yau geometry, physical theories, and data science, serving as an educational resource for new researchers.

Findings

Educational framework for Calabi-Yau manifolds

Integration of machine learning with geometric and physical concepts

Preliminary draft of a comprehensive teaching resource

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.