Sunday, August 4, 2013

M.S.NARASIMHAN ANA C.P.RAMANUJAN

 Seshachalu Narasimhan (born 1932) is an eminent Indian mathematician. He is well known along with C S Seshadri for their proof of the Narasimhan–Seshadri theorem, and both were elected as FRS.
Education.
Narasimhan did his undergraduate studies at Loyola College, Chennai, where he was taught by Fr Racine. Fr Racine had studied with the famous French mathematicians Élie Cartan and Jacques Hadamard, and connected his students with the latest developments in modern mathematics. Among Racine's other students who achieved eminence, Mudumbaiwe may count Minakshisundaram, K. G. Ramanathan, C S Seshadri, Raghavan Narasimhan, and C. P. Ramanujam.
Narasimhan went to the Tata Institute of Fundamental Research (TIFR), Bombay, for his graduate studies. He obtained his Ph.D. from University of Mumbai in 1960; his advisor was K. Chandrasekharan. Among Narasimhan's distinguished students is M. S. Raghunathan who followed in this footsteps to bag the Shanti Swarup Bhatnagar Prize as well as become FRS. Two other students who made a mark as top-notch mathematicians are S. Ramanan and V. K. Patodi.
Degrees and posts held
              Awards and felicitations
•  Visiting Scholar, Institute for Advanced Study 
   (1968-1969)
•  Fellow of the Royal Society, London
•  Head, Mathematics Group of the Abdus Salam International Centre for Theoretical Physic
   (1992–1999)
•  Honorary Fellow, Tata Institute of Fundamental Research, Bangalore Centre.
•  Third World Academy Award for Mathematics (1987)
•  Padma Bhushan (1990)
•  King Faisal International Prize for Science, 2006 (jointly with Simon Donaldson, Imperial College)
            
CP RAMANUJAM

Chakravarthi Padmanabhan Ramanujam (January 9, 1938 – October 27, 1974) worked in the fields of number theory and algebraic geometry. He was elected a Fellow of the Indian Academy of Sciences in 1973.
Like his namesake Srinivasa Ramanujan, Ramanujam also had a very short life.
As David Mumford put it, Ramanujam felt that the spirit of mathematics demanded of him not merely routine developments but the right theorem on any given topic. "He wanted mathematics to be beautiful and to be clear and simple. He was sometimes tormented by the difficulty of these high standards, but in retrospect, it is clear to us how often he succeeded in adding to our knowledge, results both new, beautiful and with a genuinely original stamp".
Career
Ramanujam set out for Mumbai at the age of eighteen to pursue his interest in mathematics. He and his friend and schoolmate Raghavan Narasimhan, and S. Ramanan joined TIFR together in 1957. At the Tata Institute there was a stream of first rate visiting mathematicians from all over the world. It was a tradition for some graduate student to write up the notes of each course of lectures. Accordingly, Ramanujam wrote up in his first year, the notes of Max Deuring's lectures on Algebraic functions of one variable. It was a nontrivial effort and the notes were written clearly and were well received. The analytical mind was much in evidence in this effort as he could simplify and extend the notes within a short time period. "He could reduce difficult solutions to be simple and elegant due to his deep knowledge of the subject matter" states Ramanan. "Max Deuring's lectures gave him a taste for Algebraic Number Theory. He studied not only algebraic geometry and analytic number theory of which he displayed a deep knowledge but he became an expert in several other allied subjects as well".
On the suggestion of his doctoral advisor, K. G. Ramanathan, he began working on a problem relating to the work of the German number theorist Carl Ludwig Siegel. In the course of proving the main result to the effect that every cubic form in 54 variables over any algebraic number field K had a non-trivial zero over that field, he had also simplified the earlier method of Siegel. He took up Waring's problem in algebraic number fields and got interesting results. In recognition of his work and his contribution to Number Theory, the Institute promoted him as Associate Professor. He protested against this promotion as 'undeserved', and had to be persuaded to accept the position. He proceeded to write his thesis in 1966 and took his Doctoral examination in 1967. Dr. Siegel who was one of the examiners was highly impressed with the young man's depth of knowledge and his great mathematical abilities.
Ramanujam was a scribe for Igor Shafarevich's course of lectures in 1965 on minimal models and birational transformation of two dimensional schemes. Professor Shafarevich subsequently wrote to say that Ramanujam not only corrected his mistakes but complemented the proofs of many results. The same was the case with Mumford's lectures on abelian varieties which was delivered at TIFR around 1967. Mumford wrote in the preface to his book that the notes improved upon his work and that his current work on abelian varieties was a joint effort between him and Ramanujam. A little known fact is that during this time he started teaching himself German, Italian, Russian and French so that he could study mathematical works in their original form. His personal library contained quite a few non-English mathematical works.

                                               DONE BY
                                                         SUCHITRA

No comments:

Post a Comment