Abstract : Geometric or physical objects often have a global, as well as a local, picture. General relativity has, in one aspect, Special relativity as a local manifestation. A surface for example can be straightened out locally, but we cannot do it simultaneously everywhere. But in both these cases, one is curved and the other flat.
Certain properties are thus reflected in the local picture, but others not. Thus 'local' may have different connotations in different studies. I will try and illustrate this with examples and finally look for a common structure, which will encompass all these as particular cases.
About the Speaker: Professor S Ramanan did his PhD at the Tata Institute of Fundamental Research, under the direction of famous mathematician Prof. M S Narasimhan, with whom he collaborated for decades. He did his post-doctoral studies at Oxford University, Harvard University and ETH Zurich.
He has made substantial contributions in the areas of Algebraic Geometry, Differential Geometry, Lie groups and Homological Algebra.
He is an internationally reputed mathematician and has been a visiting Professor at many of the world's leading universities, including Harvard University, University of California at Berkeley, the Institute of Advanced Study in Princeton, UCLA, Oxford University, Cambridge University, the Max Planck Institute, University of Paris, Kyoto University, Consejo Scientificas in Madrid, ETH Zurich, KIAS in Seoul, etc.
Prof S. Ramanan retired several years ago as a Distinguished Professor from Tata Institute of Fundamental Research. Since then he has been teaching undergraduates and graduates at IMSc, CMI and IIT Madras and also advising Ph.D. students.
Among other things, he was a recipient of the Bhatnagar award, Third World Academy of Sciences Prize for Mathematics, Ramanujan Bicentenary Medal, ... and is a Fellow of all the three academies of sciences in India (INSA, IASc, and NASc). More than all these, he is proud that most of his Ph.D. students established themselves later as fine mathematicians, and many of them received the Bhatnagar prize for instance.