|Title:||A (Brief) History of (Metric) Geometry|
|Speaker:||Bourguignon, Jean Pierre|
|Group/Series/Folder:||Record Group 8.15 - Institute for Advanced Study|
Series 3 - Audio-visual Materials
|Location:||8.15:3 box 1.5|
|Notes:||Institute for Advanced Study Distinguished Lectures.|
Abstract: Geometry is one of the oldest branches of mathematics that has accompanied the evolution of the concept of space in different cultures over centuries. Euclidean Geometry was long considered to provide the only possible model for space even after the revolution of Analytic Geometry by René Descartes. After decisive work by Carl Friedrich Gauss introducing the fundamental concept of intrinsic curvature, in the early XIXth century, non-Euclidean geometries were conceived and finally accepted, opening up considerably the horizon for Geometry. Bernhard Riemann broadened the concept even further and laid the foundations of what is now called 'Riemannian geometry' that could serve, some 50 years later after a further extension, as a model for a dynamic space-time in Einstein's Theory of General Relativity. The broadening of Geometry went even further in the late XIXth century and the early XXth century with the recognition of the intimate relation of Group Theory with Geometry, creating a new fundamental linkage.In the second part of the XXth century, wider generalizations were introduced by Alexander Alexandrov and Mikhail Gromov allowing to discuss the curvature of non-smooth spaces, and to realise the importance of the study of more general metric spaces to understand more traditional geometries. Another generalisation that borrowed some of the fundamental ideas of Quantum Mechanics was introduced by Alain Connes, in the form of Non-Commutative Geometry, providing even more sophisticated models for what could be a quantum space, covering at the same time discrete and continuous spaces.
Duration: 62 min.
|Appears in Series:||8.15:3 - Audio-visual Materials|
Videos for Public -- Distinguished Lectures