Nankai Symposium on Mathematical Dialogues
Description
This volume is the proceedings of a special conference dedicated to the legacy of Prof. S.-S. Chern, virtually held at the Chern Institute of Mathematics, Nankai University. The conference lasted 2 weeks, and included more than 80 talks, highlighted by a special public lecture by Sir Roger Penrose, on his Nobel winning work on black-holes.
The talks ranged from string theory to number theory, from algebraic geometry to muon detectors, from machine-learning to category theory, etc., all intended to be colloquium-style talks lasting 45 min each. Prof. Chern was a huge proponent and influential figure in "Mathematical Dialogues" and the wide range of topics and discussions are in this spirit.
This book is appealing to mathematicians at the PhD level who are eager to learn about how interesting mathematics show up in different fields, especially geometry, theoretical physics, number theory and modern data science.
Chapter "On Lie Algebras in Characteristic p" is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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Persons
Professor Yang-Hui He is a Fellow of the London Institute for Mathematical Sciences, housed in the Michael Faraday suites in the Royal Institute of Great Britain; professor of mathematics at City, University of London; Tutor in mathematics at Merton College, University of Oxford; and Chang-Jiang Chair of physics at Nankai University. He works at the interface of string theory, algebraic and combinatorial geometry, and was one of the pioneers in introducing machine learning to theoretical physics and pure mathematics.
Professor Mo-Lin Ge is a professor at the Chern Institute of Mathematics, Nankai University, China. He is also an Academician of Chinese Academy of Science. He has a long and distinguished career in the field of theoretical physics since the 1960s and has made many contributions to mathematical physics.
Professor Chengming Bai is a professor and current director at the Chern Institute of Mathematics, Nankai University, China. He has been interested in the study of certain algebraic systems which are related to mathematical physics and Lie theory, and their applications.
Jiakang Bao is a PhD student at City, University of London under the supervision of Prof. Y.-H. He, and a visiting researcher at the London Institute for Mathematical Sciences. His current research interests lie primarily in quiver gauge theories and BPS algebras, in the interface between theoretical physics, algebraic geometry and number theory.
Edward Hirst is a Doctoral researcher at City, University of London with Professor Y.-H He and a visiting researcher at the London Institute for Mathematical Sciences. He examines mathematical objects within theoretical physics, focusing on those related to string and gauge theories as well as the related algebraic geometry, in particular Calabi-Yau manifolds. His current work centres on applications of a variety of techniques from machine learning to databases ofthese objects, with the aim of uncovering interesting phenomena and interrelations. He will start his postdoctoral fellowship at Queen Mary, University of London.
Content
Space-Time Singularities and Cyclic Geometry: Public Lecture. Commemorating Professor S.-S. Chern's 110th.- Vanishing Yukawa Couplings and the Geometry of String Theory Models.- Calabi-Yau Genus-One Fibrations and Twisted Dimensional Reductions of F-theory by Lara Anderson, James Gray, Paul-Konstantin Oehlmann.- Calabi-Yau metrics, CFTs and random matrices.- Why Do We Care about Mahler Measure in Physics?.- Mirror Symmetry, Born Geometry and String Theory.- Double copying Exceptional Field theories.- Affine Grassmannians and Brane Systems.- Two Applications of Lie Alagebras In Characteristic p > 0.- Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology.- Computation and Data in the Classification of Fano Varieties.- Quantum cluster varieties, scattering diagrams, and the deformed Poisson families- (K)not machine learning.- Holographic State Complexity from Group Cohomology.- Duality in Hyperk¨ahler geometry.- A sheep in wolf 's clothing: from group theory to a novel antiviral strategy.- 2d Supersymmetric Gauge Theories, D-branes and Trialities.- On a matrix element representation of special functions associated with toric varieties.- Univalent Foundations.- Applications of numerically solving polynomial systems.