Langlands biography

March 21, Retrieved July 26, Langlands January American Journal of Mathematics. CiteSeerX JSTOR MR Pure Math. Institute of Advanced Studies. Annals of Mathematics Studies, Princeton University Press, Princeton, N. National Academy of Sciences. Retrieved February 13, The Abel Prize. Retrieved July 22, Royal Society of Canada. Retrieved April 3, Royal Society.

Retrieved March 22, Retrieved June 14, Archived from the original on June 29, Retrieved March 1, The Governor General of Canada. Archived from the original on June 28, Retrieved June 27, Montreal Gazette.

Langlands biography

It remains a research program for the future in all these areas. Robert Langlands and Richard Taylor jointly received the Shaw Prize in [ 59 ] :- Robert Langlands initiated a unifying vision of mathematics that has greatly extended the legacy of the mathematics of previous centuries, connecting prime numbers with symmetry. This unification, which grew out of the Reciprocity Theory of Gauss and Hilbert , is now referred to as the Langlands program.

It provides a direction of research which has guided mathematicians over the past forty years and will continue to do so for years to come. After winning the prize, Langlands gave the lecture Reflections on receiving the Shaw prize see [ 31 ]. Balasubramanian Sury wrote in a review of this paper [ 63 ] :- This is the text of a lecture delivered in Hong Kong on the occasion of the author receiving the Shaw Prize.

It makes for absolutely fascinating reading. The contents of the masterly exposition are so riveting that it is scarcely possible to put the article down without finishing it. Therefore, instead of giving a detailed description of the contents, the reviewer encourages the interested reader to peruse the text himself by just quoting the following text from the article: "a number of mathematicians have a perception of the development of the theory of automorphic forms over the last four decades that differs from mine if not in a radical, certainly in an essential way.

Some of the differences are a result of misapprehensions that are a natural consequence of the variety of the theory's relations to fields practiced by mathematicians with many different temperaments and training. With a little explanation these misapprehensions can be dissipated. The prize is an opportunity to do so. Others are the result of conflicting methodological stances, mostly unrecognised and certainly unresolved.

Their resolution will certainly demand a deeper understanding of the subject than is yet available. In this lecture I attempt to describe the current, unresolved situation. My emphasis will be on my own stance, although my purpose here is not to advocate but to explain it. The short citation reads:- Professor Langlands secured his place in history of mathematics as the proposer in and first developer of the eponymous research programme.

The deep results and visionary conjectures of the Langlands Programme relate the core themes in number theory and representation theory. The full citation begins [ 55 ] :- Robert Langlands is one of the giants of modern mathematics. By combining great technical power with extraordinary imagination and vision, he has shown how to unify major areas of mathematics that were previously believed to be quite distinct.

More precisely, Langlands has transformed the traditional area of automorphic forms, originally a part of the theory of complex variables, into a very different theory whose classical roots are now almost unrecognisable. In Langlands' hands, the theory of automorphic forms has become a grand force for unification, representing what seem to be the fundamental laws of mathematical symmetry.

These laws govern the internal structure of many diverse parts of mathematics, most notably from number theory and arithmetic algebraic geometry. The Abel Prize is recognised as the highest possible award to a mathematician. It was presented to Langlands in [ 51 ] He was then a 30 -year-old associate professor at Princeton, working during the Christmas break.

His letter introduced a theory that created a completely new way of thinking about mathematics: it suggested deep links between two areas, number theory and harmonic analysis, which had previously been considered as unrelated. Langlands' insights were so radical and so rich that the mechanisms he suggested to bridge these mathematical fields led to a project named the Langlands program.

The program has enlisted hundreds of the world's best mathematicians over the last fifty years. No other project in modern mathematics has as wide a scope, has produced so many deep results, and has so many people working on it. Its depth and breadth have grown and the Langlands program is now frequently described as a grand unified theory of mathematics.

He continued to receive honours, for example he was appointed Companion of the Order of Canada in and on 10 January Semiahmoo High School installed a mural celebrating his contributions to mathematics. Casselman, in [ 44 ] , ends with the following summary:- [ Langlands' ] astounding insight has provided a whole generation of mathematicians working in automorphic forms and representation theory with a seemingly unlimited expanse of deep, interesting, and above all approachable problems to work away on.

In the interview [ 13 ] the final question was whether Langlands had non-mathematical passions or interests of some sort. He replied:- Passions? I don't have any passions. But, you know, it is true that you want to take a look at other things, you know. He spent a good deal of time in the late eighties and nineties and with some success studying lattice models of statistical physics and the attendant conformal invariance.

In recent years, he has been preoccupied by the geometric theory of automorphic forms. He has only now reached the stage at which he can contemplate publication. Abel Prize , Wolf Prize , Breadcrumb Home Scholars Robert P. Robert P. Langlands Professor Emeritus. It may take days to find the small error. Langlands received his Ph. It was an experience I will never forget.

I was never someone who ever learned to be silent, and I remember telling him my ideas, and they were foolish ideas, I must say. Langlands had been making calculations when he came across some L-functions that he liked. He told Weil what he was thinking and Weil suggested he write it down for him. Langlands went home and wrote a seventeen-page handwritten letter, showing it to Harish-Chandra before sending it on to Weil.

In his letter, Langlands proposed a grand unifying theory that relates seemingly unrelated concepts in number theory , algebraic geometry , and the theory of automorphic forms. The geometric Langlands program, created by Vladimir Drinfeld and collaborators, is particularly rich for implications in theoretical physics, especially string theory.

Last year, Edward Witten , Charles Simonyi Professor in the School of Natural Sciences, who says his understanding of the Langlands program is limited see below wrote a page paper on the relation of part of the geometric Langlands program to physics. I think I would like to. At first, I wanted to understand it out of curiosity but now I think there are other reasons for wanting to understand it.