Tuesday, January 26, 2010

Harish Chandra

Harish Chandra was a renowned physicist and mathematician of India. His father Chandrakishore was a civil engineer. Harish Chandra spent his childhood at his maternal grandfather's home in Kanpur. At an early age he received education from a tutor. He studied at Christ Church High School till the age of fourteen, and passed his intermediate degree from Kanpur. He went to the University of Allahabad and studied theoretical physics, influenced by Dirac's Principles of Quantum Mechanics. He passed graduation in 1941 and achieved master's degree in 1943. He was a postgraduate research fellow under the supervision of Homi Bhabha on problems in theoretical physics, at the Indian Institute of Science at Bangalore. He married Lalitha Kale and had two daughters. Harish Chandra grew up in the state of Uttar Pradesh. As a very bright student in his MSc Physics class at Allahabad University, he solved the theory of the vibration of themridangam on the spot as the only question in his Acoustics exam paper, with Prof C V Raman as the examiner and received 100 marks for it. Until then only Prof C V Ramanhad worked this out and had not published it. This convinced Dr K S Krishnan, the headof the department of physics at Allahabad University and Dr C V Raman, the Director ofthe Indian Institute of Science, Bangalore that a very brilliant scholar was found. They recommended Harish Chandra to Dr Homi Bhabha who had recently returned to India from England after his PhD with Paul Dirac on the theory of the spin 3/2 particle.Homi Bhabha soon realized the ability of his first student Harish Chandra, and after somestudy with himself, recommended him to Prof Paul Dirac at Cambridge University. Hewas asked to solve the unitary representations of the Lorentz group for a PhD thesis.Until then only Dr Eugene Wigner, the brother-in –law of Dr P.A.M. Dirac had solved the problem , as well as work by Gelfand, Naimark and Bargmann. Harish Chandra developed his own approach to representations of non compact groups like the Lorentzgroup and the associated Fourier or harmonic analysis. This impressed both Dirac andWigner that Harish Chandra took just around two years to develop on his own a newapproach in group theory and use it for the Lorentz group.When asked by Paul Dirac whether it is necessary that the problem he works on and thesolution he finds have to be associated to physics while the method of work is of Mathematics, Harish Chandra said that it is not necessary that physics be the source orend point of his work, but mathematics was essential. Then he was recommended to become a mathematician and he went to Princeton where he remained all his life. LikeHermann Weyl and Elie Cartan before him, Harish Chandra made fundamentalcontributions to group theory, particularly to Lie algebras. Several programs inMathematics such as the Langlands program have arisen as a result of Harish Chandra’swork. The Institute at Allahabad is named as the Harish Chandra research Institute in his memory.K S Krishnan was Harish Chandra's teacher at Allahabad University; he recommended his name to Dirac for research work at Cambridge for his Ph.D. degree. In 1945, Harish-Chandra studied for his doctorate degree at Gonville and Caius College, Cambridge, under Dirac's supervision. However, he was not quite satisfied with Dirac's lectures when he realized that Dirac was actually reading from his books. During his days in Cambridge, he started to loose interest in Physics and took more interest in mathematics and attended the lecture courses of Littlewood and Hall. While attending a lecture by Pauli, he pointed out an error in Pauli's work. Later Pauli and Harish Chandra became very close friends. In 1947, he received his doctorate degree for his thesis 'Infinite irreducible representations of the Lorentz group. In the thesis he gave "a complete classification of the irreducible unitary representations of SL(2,C)". Harish Chandra accompanied Dirac to Princeton from 1947 to 1948 and worked as his assistant. During his stay at United States, the leading mathematicians Weyl, Artin and Chevalley who were working there had great impact on him. He remained at Princeton for another year even after Dirac came back to Cambridge. At Harvard from 1949-50, he was influenced by Zariski.. Harish Chandra was a faculty at the Columbia University from 1950-63, this duration is considered to be the most productive period of his career where he worked on representations of semisimple Lie groups. During this period he worked in many institutions. From 1955-56 he was at the Institute for Advanced Study at Princeton, from 1957-58 as a Guggenheim Fellow in Paris. Harish Chandra formulated a fundamental theory of representations of Lie groups and Lie algebras. He even extended the concept of a characteristic representation of finite-dimensional of semisimple Lie groups to infinite-dimensional representations of a case and formulated a Weyl's character formula analogue. Some of his other contributions are: the specific determination of the Plancherel measure for semisimple groups, the evaluation of the representations of discrete series, based on the results of Eisenstein series and in the concept of automorphic forms, his "philosophy of cusp forms", including the real Lie groups, but also p-adic groups or groups over adele rings. While working at the Institute of Advanced Study at Princeton from 1963, he was appointed IBM-von Neumann Professor in 1968. Harish Chandra received many eminent awards as:
AMS Cole Prize in Algebra (1954)
Speaker at International Congress (1954)
AMS Colloquium Lecturer (1969)
Fellow of the Royal Society (1973)
Ramanujan Medal from Indian National Science Academy.(1974)
Honorary degrees by Delhi University (1973) and Yale University (1981)
Fellow of the National Academy of Sciences (United States) (1981) He was participating in a conference in Princeton when he died on Sunday 16th October1983, due to a heart attack.

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