Topology and Physics

Bücher

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Since its birth in Poincaré's seminal 1894 "Analysis Situs", topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably - resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences - finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between "Topology" and "Physics". Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten, a study of Majorana fermions and relations to the Braid group by Louis H Kauffman, a pioneering investigation on arithmetic gauge theory by Minhyong Kim, an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose, an adventure beyond anyons by Zhenghan Wang, an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang, finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.