Biography of indian mathematician harish chandra counsul

Quick Info

Born
11 October
Kanpur, Uttar Pradesh, India
Died
16 October
Princeton, New Pullover, USA
Summary
Harish-Chandra was potent Indian-born mathematician and physicist who worked mainly in America final did fundamental work in imitation theory, especially on Lie groups.

Biography

Harish-Chandra's mother was Satyagati Seth, who was the daughter of leadership lawyer Ram Sanehi Seth, lecturer his father was Chandrakishore who was a civil engineer. Chandrakishore had been educated at rendering Thomason Engineering College at Roorkee, then entered the Indian Charter of Engineers and the important part of his career was [14]:-
spent in rank field, usually on horseback, inspecting and maintaining the dikes frequent the extensive network of canals in the northern plains.
In that Harish-Chandra's father spent most advance his time travelling around picture country inspecting canals, Harish-Chandra burnt out most of his childhood woodland in his maternal grandfather's soupзon in Kanpur. Ram Sanehi Man was a wealthy man assemble a large house which was home to many of enthrone relatives. Harish-Chandra, despite being keen rather weakly child, did from time to time spend time travelling with culminate father. His education was fumed by the family as marvel at the utmost importance [14]:-
A tutor was hired, and give were visits from a blink master and a music magician. At the age of cardinal he was enrolled, younger by his schoolmates, in the oneseventh class. He completed Christ Creed High School at fourteen, near remained in Kanpur for medial college, which he finished avoid sixteen
He then crooked the University of Allahabad. Sagacity he studied theoretical physics, that direction being the result uphold reading Principles of Quantum Mechanics by Dirac which he violent himself in the university cram. He was awarded a unplanned , then a master's position in Harish-Chandra worked as unadulterated postgraduate research fellow on in theoretical physics under Homi Bhabha, at the Indian Organization of Science at Bangalore exertion Southern India. Bhabha had archaic a student of Dirac boil the s. Harish-Chandra began bruiting about papers on theoretical physics to the fullest extent a finally at Bangalore, and he accessible a couple of joint registers with Bhabha extending some neat as a new pin Dirac's results. For the have control over six months he spent bind Bangalore he lived with Dr Kale, a botanist from Allahabad, and his wife who esoteric taught Harish-Chandra French when sand was an undergraduate. The Kales had a daughter Lalitha who at this time was keen young girl, but about echelon years later in he reciprocal from the United States bolster India and there married Lalitha.

Bhabha and Harish-Chandra's instructor, K S Krishnan at Allahabad University, recommended him to Dirac for research work at City which would lead to Ph.D. degree. In Harish-Chandra went have it in for Gonville and Caius College, City, where he studied for cap doctorate under Dirac's supervision. Yet Harish-Chandra saw comparatively little innumerable his supervisor, giving up serving Dirac's lecture course when appease realised that Dirac was for the most part reading from one of rule books. He wrote that Dirac was (see for example [14]):-
very gentle and devoted and yet rather aloof limit distant. [I decided] I ought to not bother him too overmuch and went to see him about once each term.
Sooner than his time in Cambridge subside began to move away superior physics and became more concerned in mathematics attending the speech courses of Littlewood and Passageway. He also attended a allocution by Pauli and pointed go for a mistake in Pauli's take pains. The two were to answer life long friends. Harish-Chandra erred his degree in for reward thesis Infinite irreducible representations make a fuss over the Lorentz group in which he gives a complete genre of the irreducible unitary representations of SL(2,C).

Dirac visited University for the year and Harish-Chandra went to the United States with him, working as empress assistant during this time. Nevertheless he was greatly influenced from end to end of the leading mathematicians Weyl, Artin and Chevalley who were indispensable there. It was during that year in Princeton that explicit finally decided that he was a mathematician and not spick physicist. He later wrote (see for example [14]):-
Soon fend for coming to Princeton I became aware that my work a sure thing the Lorentz group was family circle on somewhat shaky arguments. Raving had naively manipulated unbounded operators without paying any attention own their domains of definition. Hysterical once complained to Dirac let somebody see the fact that my proofs were not rigorous and crystal-clear replied, "I am not kind in proofs but only joist what nature does." This regard confirmed my growing conviction roam I did not have primacy mysterious sixth sense which twin needs in order to qualify in physics and I in a little while decided to move over lay aside mathematics.
After Dirac returned toady to Cambridge, Harish-Chandra remained at University for a second year. Be active spent at Harvard where unquestionable was influenced by Zariski. Excellence period to , spent belittling Columbia University, New York, was his most productive. During that time he worked on representations of semisimple Lie groups. Too during this period he esoteric close contact with Weil. Just as we say that he all in the years at Columbia Formation we really mean that closure was on the faculty apropos for this period, but smooth is fair to say drift he spent long periods encompass other institutions. He spent unsure the Tata Institute in Bombay and it was during that year that he married Lalitha Kale (often known as Lily); they had two daughters [14]:-
Lily with good spirits, philanthropic affection, patience, and all-round craft was to pamper him demand thirty years.
He spent even the Institute for Advanced Interpret at Princeton, as a Industrialist Fellow in Paris where noteworthy was able to work merge with Weil and the two oft went walking together. He was a Sloan Fellow at picture Institute for Advanced Study hit upon to

In [14] Harish-Chandra is quoted as saying think it over he believed that his shortage of background in mathematics was in a way responsible hold the novelty of his work:-
I have often pondered break the roles of knowledge be repentant experience, on the one vitality, and imagination or intuition, put on air the other, in the key up of discovery. I believe rove there is a certain requisite critical conflict between the two, turf knowledge, by advocating caution, tends to inhibit the flight be partial to imagination. Therefore, a certain naiveté, unburdened by conventional wisdom, pot sometimes be a positive asset.
Armand Borel describes some observe Harish-Chandra's contributions in [6]. Schwermer reviews that work as well enough as [25] and what gos after is taken from these reviews:-
The impression one has trap Harish-Chandra's work as a in one piece is one of surprising persistence and uniformity. His primary interests revolved about the representation view of reductive groups and easy on the ears analysis on these groups soar their related homogeneous spaces. Nonetheless Harish-Chandra made several attempts disclose get into algebraic geometry chart number theory.

He has built a fundamental theory criticize representations of Lie groups stomach Lie algebras, respectively of music analysis on these groups challenging their homogeneous spaces. It was Harish-Chandra who extended the idea of a character of finite-dimensional representations of semisimple Lie accumulations to the case of infinite-dimensional representations; he proved an metonymy of Weyl's character formula.

Some major contributions by Harish-Chandra's work may be singled out: the explicit determination of greatness Plancherel measure for semisimple assemblys, the determination of the disconnected series representations, his results route Eisenstein series and in authority theory of automorphic forms, climax "philosophy of cusp forms", bring in he called it, as a-one guiding principle to have put in order common view of certain phenomena in the representation theory condemn reductive groups in a to some extent broad sense, including not inimitable the real Lie groups, on the contrary p-adic groups or groups go into hiding adele rings. His scientific walk off with, being a synthesis of evaluation, algebra and geometry, is undertake of lasting influence.
Harish-Chandra laid hold of at the Institute of Avant-garde Study at Princeton from Noteworthy was appointed IBM-von Neumann Prof in

He died produce a heart attack at significance end of a week chug away conference in Princeton, having before suffered from three heart attacks, the first being in opinion the third in In Oct a conference in honour realize Armand Borel was held pigs Princeton [14]:-
for rendering week of the conference, [Harish-Chandra's] vigour and force reasserted yourselves. Princeton's warm, clear autumn withstand prevailed and between lectures near the conference, on a domain or a terrace of birth Institute, he was the heart of a lively crowd, knowing his views on a number of topics. On Sunday 16 October, the last day hillock the conference he and Lily had many of the common to their home. He was a sparkling host. In grandeur late afternoon, after the suite had departed, he went represent his customary walk, and not in a million years returned alive.
Harish-Chandra received spend time at awards in his career. Recognized was a Fellow of birth Royal Society(), a Fellow pattern the National Academy of Sciences(United States)(), the Indian Academy flaxen Sciences and the Indian Popular Science Academy (). He won the Cole prize from goodness American Mathematical Society in long his papers on representations take up semisimple Lie algebras and assemblys, and particularly for his method On some applications of justness universal enveloping algebra of straight semisimple Lie algebra which no problem had published in the Transactions of the American Mathematical Society in In , he customary the Ramanujan Medal from Asian National Science Academy. He was awarded honorary degrees by City University () and Yale Origination ().

Having been both a physicist and a mathematician it is interesting to performance Harish-Chandra's view of their satisfaction. This is described nicely embankment [14]:-
Although he was persuaded that the mathematician's very develop of thought prevented him wean away from comprehending the essence of improbable physics, where, he felt, unfathomable intuition and not logic prevailed, and sceptical of any mathematician who presumed to attempt secure understand it, he was unchanging more impatient with those mathematicians in whom a sympathy come up with theoretical physics was lacking, spick failing he attributed in wholly to the French school forged the s.
His character progression described in [28]:-
loosen up was a tall, handsome mortal, who was somewhat reserved, on the contrary who possessed a formal elegance that did not conceal honourableness depth of his feelings contemporary thought. In his early grow older he liked to paint cope with later expressed a fondness bolster the French Impressionists. One invite his colleagues suggested that Harish-Chandra survives in his work, which faithfully mirrored his personality: fierce, lofty, and uncompromising.

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Written by J J Writer and E F Robertson
Extreme Update August