Dialogues Between Physics and Mathematics C. N. Yang at 100

This volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science.

Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.

Inspired by the original ideas of C. N. Yang, this unique collection of papers by masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.

1 Frank Yang at Stony Brook and the Beginning of Supergravity.- 2. A Stacky Approach to Crystals.- 3 The Potts Model, the Jones Polynomial and Link Homology.- 4 The Penrose–Onsager–Yang Approach to Superconductivity and Superfluidity.- 5 Quantum Operads.- 6 Quantum computational complexity with
photons and linear optics.- 7 Quantized Twistors, G2*, and the Split Octonions.- 8 Kronecker Anomalies and Gravitational Striction.- 9 Projecting Local and Global Symmetries to the Planck Scale.- 10 Gauge Symmetry in Shape Dynamics.- 11 Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.- 12 Quantum Anomalous Hall Effect.- 13 Magic Superconducting States in Cuprates.

Mo-Lin Ge is Professor at the Chern Institute of Mathematics at Nankai University, China, and academician at the Academy of Science of China. His main research topics are at the interface between theoretical physics and related mathematics, such as Yang–Mills theory and Yang–Baxter systems, especially their applications in physics. He established the Theoretical Physics Section at the Chern Institute, supervised by Prof. C. N. Yang, which has since become one of the global communication centres for mathematical physics.

 

Yang-Hui He is a Fellow of the London Institute, Professor of Mathematics at City, University of London, Tutor in Mathematics at Merton College, Oxford, and Chang-Jiang Chair of Physics at Nankai University in China. He obtained his BA at Princeton (summa cum laude, Shenstone Prize and Kusaka Prize), MA at Cambridge (Distinction, Tripos), and PhD at MIT. After a postdoc at the University of Pennsylvania, he joined Oxford as the FitzJames Fellow and an STFC Advanced Fellow. He works at the interface of string theory, algebraic and combinatorial geometry, and machine learning; he is also a keen public communicator of mathematics and physics.