Title: Euclidean Geometry, Analysis and Physics
Speaker: Professor Nitin Nitsure, Professor of Mathematics, Tata Institute of Fundamental Research, Mumbai
Abstract: Pythagoras and Euclid had limited tools, but unlimited curiosity. Understanding interesting geometric objects and phenomena beyond triangles and circles and their intersections needs more sophisticated tools (technology) from algebra and analysis. These tools were developed only in the last three hundred years. Modern functional analysis, Lie groups and representation theory may be seen as natural continuations of what Pythagoras and Euclid started. Some of the most interesting features of the progress of Euclidean geometry were repeated at an accelerated rate in the development of special relativity and relativistic quantum theory, almost as if "ontogeny recapitulates phylogeny" in the words of biologists. What took more than two thousand years in the history of Euclidean geometry was in some sense repeated in modern physics just in the span of about 50 years! This talk will give an overview of this surprising history ranging from Pythagoras (500 BC) to Wigner (1940), and a popular account of the new tools from algebra and analysis which made the modern progress possible.