Biography of indian mathematician harish chandra mathematician

Quick Info

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

Biography

Harish-Chandra's mother was Satyagati Seth, who was the daughter of greatness lawyer Ram Sanehi Seth, soar his father was Chandrakishore who was a civil engineer. Chandrakishore had been educated at honourableness Thomason Engineering College at Roorkee, then entered the Indian Utility of Engineers and the primary part of his career was [14]:-
spent in rank field, usually on horseback, inspecting and maintaining the dikes be in the region of the extensive network of canals in the northern plains.
Thanks to Harish-Chandra's father spent most light his time travelling around rectitude country inspecting canals, Harish-Chandra drained most of his childhood extant in his maternal grandfather's children's home in Kanpur. Ram Sanehi Man was a wealthy man exchange a large house which was home to many of sovereignty relatives. Harish-Chandra, despite being unmixed rather weakly child, did occasionally spend time travelling with sovereign father. His education was instant by the family as stare the utmost importance [14]:-
A tutor was hired, and present were visits from a sparkling master and a music bravura. At the age of ennead he was enrolled, younger go one better than his schoolmates, in the ordinal class. He completed Christ Sanctuary High School at fourteen, vital remained in Kanpur for inner college, which he finished decay sixteen
He then traumatic the University of Allahabad. In he studied theoretical physics, that direction being the result insinuate reading Principles of Quantum Mechanics by Dirac which he set up himself in the university survey. He was awarded a disintegration , then a master's distinction in Harish-Chandra worked as straighten up postgraduate research fellow on crushing in theoretical physics under Homi Bhabha, at the Indian School of Science at Bangalore detain Southern India. Bhabha had bent a student of Dirac inconvenience the s. Harish-Chandra began making known papers on theoretical physics decide at Bangalore, and he available a couple of joint registers with Bhabha extending some glimpse Dirac's results. For the control six months he spent unimportant Bangalore he lived with Dr Kale, a botanist from Allahabad, and his wife who esoteric taught Harish-Chandra French when forbidden was an undergraduate. The Kales had a daughter Lalitha who at this time was swell young girl, but about character years later in he reciprocal from the United States flesh out India and there married Lalitha.

Bhabha and Harish-Chandra's educator, K S Krishnan at Allahabad University, recommended him to Dirac for research work at University which would lead to Ph.D. degree. In Harish-Chandra went distribute Gonville and Caius College, City, where he studied for rule doctorate under Dirac's supervision. Despite that Harish-Chandra saw comparatively little eliminate his supervisor, giving up gate Dirac's lecture course when subside realised that Dirac was largely reading from one of books. He wrote that Dirac was (see for example [14]):-
very gentle and fast and yet rather aloof famous distant. [I decided] I must not bother him too wellknown and went to see him about once each term.
Nearby his time in Cambridge inaccuracy began to move away running off physics and became more affected in mathematics attending the address courses of Littlewood and Foyer. He also attended a discourse by Pauli and pointed snag a mistake in Pauli's enquiry. The two were to alter life long friends. Harish-Chandra erred his degree in for culminate thesis Infinite irreducible representations go rotten the Lorentz group in which he gives a complete ilk 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 circlet assistant during this time. Quieten he was greatly influenced by way of the leading mathematicians Weyl, Artin and Chevalley who were running there. It was during that year in Princeton that inaccuracy finally decided that he was a mathematician and not neat as a pin physicist. He later wrote (see for example [14]):-
Soon puzzle out coming to Princeton I became aware that my work verbal abuse the Lorentz group was household on somewhat shaky arguments. Crazed had naively manipulated unbounded operators without paying any attention respect their domains of definition. Funny once complained to Dirac nearly the fact that my proofs were not rigorous and noteworthy replied, "I am not curious in proofs but only comport yourself what nature does." This speak confirmed my growing conviction wander I did not have character mysterious sixth sense which individual needs in order to take the place of in physics and I betimes decided to move over arranged mathematics.
After Dirac returned prefer Cambridge, Harish-Chandra remained at Town for a second year. Forbidden spent at Harvard where explicit was influenced by Zariski. Justness period to , spent luck Columbia University, New York, was his most productive. During that time he worked on representations of semisimple Lie groups. Further during this period he esoteric close contact with Weil. Just as we say that he drained the years at Columbia Academy we really mean that recognized was on the faculty near for this period, but bill is fair to say renounce he spent long periods distort other institutions. He spent power 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, toothsome acceptable affection, patience, and all-round capacity was to pamper him mention thirty years.
He spent exceed the Institute for Advanced Glance at at Princeton, as a Philanthropist Fellow in Paris where be active was able to work look into Weil and the two frequently went walking together. He was a Sloan Fellow at say publicly Institute for Advanced Study pass up to

In [14] Harish-Chandra is quoted as saying digress he believed that his failure of background in mathematics was in a way responsible pine the novelty of his work:-
I have often pondered ignore the roles of knowledge omission experience, on the one lunchhook, and imagination or intuition, categorize the other, in the shape of discovery. I believe go off there is a certain main conflict between the two, arena knowledge, by advocating caution, tends to inhibit the flight show imagination. Therefore, a certain naiveté, unburdened by conventional wisdom, throng together sometimes be a positive asset.
Armand Borel describes some be worthwhile for Harish-Chandra's contributions in [6]. Schwermer reviews that work as chuck as [25] and what gos next is taken from these reviews:-
The impression one has have a phobia about Harish-Chandra's work as a taken as a whole is one of surprising ropiness and uniformity. His primary interests revolved about the representation inkling of reductive groups and sweet-sounding analysis on these groups extremity their related homogeneous spaces. Banish Harish-Chandra made several attempts undertake get into algebraic geometry find time for number theory.

He has built a fundamental theory be defeated representations of Lie groups become calm Lie algebras, respectively of music analysis on these groups current their homogeneous spaces. It was Harish-Chandra who extended the belief of a character of finite-dimensional representations of semisimple Lie assortments to the case of infinite-dimensional representations; he proved an allusion of Weyl's character formula.

Some major contributions by Harish-Chandra's work may be singled out: the explicit determination of justness Plancherel measure for semisimple accumulations, the determination of the individual series representations, his results market Eisenstein series and in character theory of automorphic forms, authority "philosophy of cusp forms", sort he called it, as wonderful guiding principle to have practised common view of certain phenomena in the representation theory objection reductive groups in a somewhat broad sense, including not nonpareil the real Lie groups, nevertheless p-adic groups or groups stumble on adele rings. His scientific weigh up, being a synthesis of debate, algebra and geometry, is all the more of lasting influence.
Harish-Chandra laid hold of at the Institute of Late Study at Princeton from Be active was appointed IBM-von Neumann Prof in

He died model a heart attack at high-mindedness end of a week squander conference in Princeton, having beneath suffered from three heart attacks, the first being in shaft the third in In Oct a conference in honour produce Armand Borel was held imprint Princeton [14]:-
for justness week of the conference, [Harish-Chandra's] vigour and force reasserted person. Princeton's warm, clear autumn unwell prevailed and between lectures rag the conference, on a applicants or a terrace of rank Institute, he was the middle of a lively crowd, knowing his views on a mode of topics. On Sunday 16 October, the last day unmoving the conference he and Lily had many of the battleground to their home. He was a sparkling host. In honourableness late afternoon, after the actors had departed, he went patron his customary walk, and at no time returned alive.
Harish-Chandra received myriad awards in his career. Unquestionable was a Fellow of class Royal Society(), a Fellow outandout the National Academy of Sciences(United States)(), the Indian Academy stare Sciences and the Indian State Science Academy (). He won the Cole prize from primacy American Mathematical Society in shelter his papers on representations scope semisimple Lie algebras and assemblages, and particularly for his newspaper On some applications of justness universal enveloping algebra of neat semisimple Lie algebra which grace had published in the Transactions of the American Mathematical Society in In , he normal the Ramanujan Medal from Soldier National Science Academy. He was awarded honorary degrees by Metropolis University () and Yale Installation ().

Having been both a physicist and a mathematician it is interesting to examine Harish-Chandra's view of their satisfaction. This is described nicely shore [14]:-
Although he was clear that the mathematician's very course of thought prevented him escape comprehending the essence of untested physics, where, he felt, extensive intuition and not logic prevailed, and sceptical of any mathematician who presumed to attempt fro understand it, he was all the more more impatient with those mathematicians in whom a sympathy patron theoretical physics was lacking, straight failing he attributed in administer to the French school pointer the s.
His character court case described in [28]:-
proscribed was a tall, handsome squire, who was somewhat reserved, on the other hand who possessed a formal civility that did not conceal rank depth of his feelings champion thought. In his early grow older he liked to paint enjoin later expressed a fondness be thankful for the French Impressionists. One garbage his colleagues suggested that Harish-Chandra survives in his work, which faithfully mirrored his personality: excessive, lofty, and uncompromising.

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