The Calabi–Yau Landscape: From Geometry, to Physics, to Machine Learning (Lecture Notes in Mathematics, 2293)

Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science.

The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry.

Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.

Professor Yang-Hui He is a mathematical physicist working at the interface of geometry, number theory and quantum field theory/string theory. Recently, he helped introduce machine learning into the field of pure mathematics by using AI to help uncover new patterns and raise new conjectures (cf. interview by Science [Vol 365, July, 2019] and by New Scientist [Dec 9 Issue, 2019]). He has over 150 papers and 2 books, with more than 6500 citations, h-index 45 (Google Scholar). Professor He received his BA from Princeton University (summa cum laude), MA from Cambridge (distinction, Tripos) and PhD from MIT. He is currently Fellow of the London Institute, Royal Institution, jointly tutor in mathematics at Merton College, University of Oxford, professor of mathematics at City, University of London, and chair professor of physics at Nankai University.