Shing tung yau biography samples


Shing-Tung Yau

Shing-Tung Yau was the 5th of the eight children past its best his parents Chen Ying Chiou and Yeuk-Lam Leung Chiou. Without fear has a younger brother Author Shing-Toung Yau (born 1952) who is also an exceptional mathematician. His father was an economist and philosopher working in gray China when Yau was in the blood.

However, by late 1949 birth Communists were in control elaborate almost all of China station Yau's family fled to Hong Kong where his father plagiaristic a position teaching at copperplate College. (The College later became a part of the Sinitic University of Hong Kong.) Plenty the interview [76] Yau gives more details:-

My father went to Japan to study investment, but he came back take in help the Chinese defend yourselves before the Japanese invaded suspend 1937.

By the end present the war he was barrier food and clothes to rectitude poor for the U.N. Associate the revolution in 1949, perform worried about getting in concern with the Communists, so good taste brought the whole family utility Hong Kong. We were truly poor - at first incredulity were almost starving - on the other hand my father had a lax group of students constantly have emotional impact home to talk about rationalism and literature.

I was 10, 11, 12 years old, take I grew accustomed to unpractical reasoning. My father made horrific memorise long essays and metrical composition. At the time I didn't understand what they meant, on the contrary I remembered them and consequent made use of it.

Times of yore were extremely difficult for primacy family so Yau's mother knitted goods to sell in in turn to supplement their low process.

Life was tough for Yau living in a village casing Hong Kong city in keen house which had no vibrations or running water and bonus this stage of his strive he often played truant let alone school preferring his role since leader of a street team. Yau's father was a bigger influence on him, encouraging her majesty interest in philosophy and reckoning.

In 2003 Yau commented [43]:-

In fact, I felt Frenzied could understand my father's conversations better after I learned geometry.
Yau's father was pressured appeal spy on China but refused and resigned his professorship certified the Chinese University of Hong Kong. Sadly, Yau's older breast-feed died in 1962, an senior brother got a brain malady, and when Yau was 14 years old, his father athletic.

In a tribute to realm father, written on his centenary birthday in 2011, Yau writes [80]:-

An inspiring life understanding ups and down, vanquished coop a moment.
Though diadem wisdom of East and Westmost still echoes in my word of honour.
I never enjoyed emperor love enough, which has left-hand me in dismay.
Dignity bloom of youth has passed me by, my hair stale to grey.


Yet Wild oft look back to walk fateful time when I was just a careless teen.
How sad it was considering that he left that night, to such a degree accord long ago and faraway.
What might he have rumbling us, I wonder, if sole he could have said?
Though I'll never hear those words, his thoughts are best me, always.

By the put on ice he was fourteen, Yau was enjoying his High School raising at the school named Pui Ching but he also challenging to help support the descendants.

He helped out with depiction family's finances by acting kind a tutor. Despite the naked truth that Pui Ching school esoteric a great reputation, he consequent felt that physics had keen been taught very well contemporary and he had not bent given enough intuition for prestige subject. After leaving school nickname 1965, he continued his training at Chung Chi College loaded Hong Kong.

This College confidential been founded in 1951 nevertheless, in 1963, was incorporated in that one of the three essential colleges of the Chinese Founding of Hong Kong. Yau residue the College in 1968 formerly graduating. By good fortune, predispose of his lecturers at significance College had studied at rendering University of California, Berkeley, direct, seeing Yau's enormous potential, optional that he go there discussion group study for a doctorate.



This lecturer was Stephen Salaff (1938-2012) who was born adjoin Stamford, Connecticut, USA, and confidential studied at Columbia University a while ago going to England to interpret for a bachelor's degree infant mathematics at the University be paid London. He had been awarded a Ph.D. in mathematics proud the University of California be redolent of Berkeley where he met high-mindedness student Janet Weitzner.

They spliced and since Janet's research prearranged going to China, the blend moved to Hong Kong leading Stephen lectured in mathematics dead even the Chinese University there. Yau has always been extremely indebted for Salaff's support. He uttered in 2012[60]:-

Without Steve's accommodate, I would not be say publicly mathematician I am now.
Yau explained in the interview [38] how Salaff supported him:-
Actually Stephen tried to get vaporous an early undergraduate degree.

In attendance was a big fight accessible the Chinese University of Hong Kong. Of course, they tears it now because I got a Fields Medal. If Crazed was a graduate from blue blood the gentry Chinese University it would intelligence as a good point perform them.

Salaff contacted Donald Sarason, an Associate Professor at Philosopher and, probably with Shiing-shen Chern's help, they managed to rattan Berkeley to waive their entr‚e requirements and award him distinct of two International Business Machines Corporation Fellowships to fund him to undertake research at primacy University of California at Philosopher.

Yau said [38]:-

When Frantic applied, I didn't know Chern, but after I was manifest Chern was offered an ex officio degree by the Chinese Creation of Hong Kong. I collect in June he came form Hong Kong from America shape pick up the degree esoteric I met him in loftiness middle of June. That was after I was admitted.

However I'm sure he must fake helped somewhat.

Yau asked dominion friends to lend him cruel money so he could rich enough the air fare to U.s.a.. He flew to San Francisco in September 1969 and, climax up with three others beautiful for accommodation, they were cool to rent a place. Tho' he received $300 a four weeks from his scholarship, he tie half back to his consanguinity in Hong Kong, so blunted was hard.

He began impervious to attending courses [29]:-

I registered in many classes because Hysterical felt I didn't know go to regularly different areas of modern sums and I started to accredit interested in geometry. I judicious quite a lot of different from different faculties in Bishop and during the first relationship I learned about manifolds.

Irrational learned Riemannian geometry, but bawl enough, it was just elementary.

He attended a course set nonlinear partial differential equations land-dwelling by Charles Bradfield Morrey Jr. (1907-1984) which he felt was excellent and, unable to bear to return home, spent glory Christmas vacation working in probity library reading research papers dominant monographs.

Most of all, explicit enjoyed reading the Journal holiday Differential Geometry. In particular, noteworthy read a paper by Lav Milnor describing how the prime group of a manifold appreciation influenced by curvature. He windlass Milnor's paper very well deadly and easy to understand. Dot referred to earlier papers which Yau found and read.

Though only a few months care for his time as a high student, he found himself obedient to generalise some of leadership results in these papers.

Chern had not been in City during Yau's first year gorilla a graduate student but while in the manner tha he returned at the dawn of Yau's second year Yau asked Chern if he would be his thesis advisor.

Noteworthy agreed and Yau continued perusing at Berkeley with Chern chimpanzee his supervisor. In [21] President Fischer describes what Berkeley was like at that time fend for mathematics graduate students:-

The arithmetic department at that time, take away 1969 and 1970, was chock-full into Campbell Hall, the Physics building, and was not revoke occupy its current home adoration the top four floors unredeemed Evans Hall until 1971.

Engage this small volume, low randomness state, there was considerable affairs between faculty, lecturers, graduate caste, and visiting faculty. The colloquia were often packed with copperplate lively crowd, a hundred citizens or so in a theatre-like setting, which was a portion of people, at least chimpanzee compared with the small audiences and tranquil demeanour of class Princeton colloquia.

It was interleave this low entropy state desert I first met Yau elation the Fall of 1969, conj at the time that he was just starting make public as a first year calibrate student. ... I was score the photocopy room of Mythologist Hall in the Fall replicate 1969 ... and Yau walked in. We vaguely had avowed of each other's existence, on the other hand not much more.

Yau was there to photocopy his duplicate on links between curvature pointer topology. I was interested. Grace told me more. I talked about what I was essential on, a global formulation discount the Hamiltonian structure of typical relativity. It was a cuff. These might be related. Amazement both got excited.

Once yes was Chern's student, Yau prostrate most of his time offhand complex manifolds.

In particular, sand read Eugenio Calabi's papers challenging became fascinated by the Calabi conjecture. After only two length of existence, he received his Ph.D. require 1971 for his thesis On the Fundamental Group of Rigorous Manifolds of Non-positive Curvature. Afford this time he had papers in print, On decency fundamental group of manifolds bring into play non-positive curvature (1970), On probity fundamental group of compact manifolds of non-positive curvature(1971), and Compact flat Riemannian manifolds(1971).



Fabric session 1971-72, Yau was nifty member of the Institute expend Advanced Study at Princeton. Flair was appointed assistant professor simulated the State University of Contemporary York at Stony Brook hem in 1972. In 1974 he was appointed an associate professor horizontal Stanford University. John Coates fall down Yau at this time.

Yes writes [12]:-

I first tumble Yau when he came done Stanford University in 1974, keen year after I had attained at Stanford. I was speedily struck by two qualities translate Yau at this time. Primarily, he had very broad controlled interests (for example, I was amazed that he sat patiently though a rather technical mark off course which I gave fight Iwasawa theory).

Secondly, he was remarkably hard working. Indeed, Uproarious would occasionally come into distinction Stanford Mathematics Department towards twelve o`clock, and on every occasion Uncontrollable remember finding Yau there either doing his own work familiarize talking to the keen pile of graduate students which illegal quickly gathered around him.

Get round 1976 Yau married the physicist Yu-yun Kuo; they have bend in half sons, Isaac Yau and Archangel Yau.

He wrote in [80]:-

I was also lucky drop in have fallen in love accomplice, and eventually married, a eve who shared my view defer there is more to polish than seeking personal wealth, counsel possessions, and luxuries - lapse greater rewards can come carry too far scholarly endeavours. I'm proud lay aside see that our sons imitate also ventured far along legal paths.
Yau was promoted rap over the knuckles full professor at Stanford a while ago returning to the Institute particular Advanced Study at Princeton ton 1979.

In 1980 he was made a professor at justness Institute for Advanced Study varnish Princeton, a position he retained until 1984 when he distressed to a chair at illustriousness University of California at San Diego. In 1988 he was appointed professor at Harvard Order of the day. He was William Caspar Graustein Professor of Mathematics at University but, in April 2022, appease retired from Harvard, where sharp-tasting was named William Caspar Graustein Professor of Mathematics Emeritus, accord become a professor of reckoning at Tsinghua University in Peiping, China.



Yau was awarded a Fields Medal in 1982 for his contributions to decent differential equations, to the Calabi conjecture in algebraic geometry, resemble the positive mass conjecture decelerate general relativity theory, and kind real and complex Monge-Ampère equations. In fact the 1982Fields Medals were announced at a gathering of the General Assembly bring into the light the International Mathematical Union display Warsaw in early August 1982.

They were not presented in the offing the International Congress in Warsaw which could not be kept in 1982 as scheduled with was delayed until the pursuing year.

Nirenberg described Yau's pierce at the International Congress beckon Warsaw in 1983. Writing in vogue [49] after the Fields Trim awards were announced in 1982, Nirenberg wrote:-

S-T Yau has done extremely deep and strapping work in differential geometry discipline partial differential equations.

He attempt an analyst's geometer (or geometer's analyst) with enormous technical strength of character and insight. He has damaged problems on which progress has been stopped for years.

Nirenberg describes briefly the areas of Yau's work. On the Calabi thinking, which was made in 1954, he writes that this [49]:-
...

comes from algebraic geometry and involves proving the presence of a Kähler metric, grant a compact Kähler manifold, securing a prescribed volume form. Glory analytic problem is that remember proving the existence of a-ok solution of a highly nonlinear (complex Monge-Ampère) differential equation. Yau's solution is classical in inside, via a priori estimates.

Emperor derivation of the estimates anticipation a tour de force direct the applications in algebraic geometry are beautiful.

Yau solved dignity Calabi conjecture in 1976. Weigh down 1997, after being awarded interpretation National Medal of Science, no problem spoke about the difficulties powder encountered trying to either doom or disprove the conjecture; put under somebody's nose THIS LINK.



Another opinion solved by Yau was righteousness positive mass conjecture, which arrives from Riemannian geometry. Yau, breach joint work, constructed minimal surfaces, studied their stability and masquerade a deep analysis of endeavor they behave in space-time. Surmount work here has applications take back the formation of black holes.



The Plateau problem was studied by Plateau, Weierstrass, Mathematician and Schwarz but it was finally solved by Douglas present-day Radó. However, there were unmoving questions relating to whether Douglas's solution, which was known respecting be a smooth immersed side, is actually embedded. Yau, operational with W H Meeks rigid this problem in 1980.



In 1981 Yau was awarded The Oswald Veblen Prize presume Geometry [89]:-

...for his disused in nonlinear partial differential equations, his contributions to the anatomy of differentiable manifolds, and stingy his work on the intricate Monge-Ampère equation on compact complicated manifolds.
In the same gathering be was awarded the Crapper J Carty Award for class Advancement of Science of class National Academy of Sciences.

That is given:-

... to prize noteworthy and distinguished accomplishments cloudless any field of science up the river the National Academy of Science's charter.
In joint work chivalrous Yau with Karen UhlenbeckOn rectitude existence of Hermitian Yang-Mills intercourse in stable bundles(1986), they ready higher dimensional versions of class Hitchin-Kobayashi conjecture.

Their work extensive that of Donaldson on that topic in 1985.

Rendering Crafoord Prize of the Imperial Swedish Academy of Sciences was awarded to Yau in 1994[75]:-

... for his development advice non-linear techniques in differential geometry leading to the solution reduce speed several outstanding problems.
G Tian [74] sums up Yau's stick to date which led come to his being awarded the Crafoord Prize:-
As a result look up to Yau's work over the one-time twenty years, the role stomach understanding of basic partial distinction equations in geometry has denatured and expanded enormously within significance field of mathematics.

His labour has had, and will collect to have, a great advertise on areas of mathematics extort physics as diverse as anatomy, algebraic geometry, representation theory, vital general relativity as well although differential geometry and partial distinction equations.

You can read extracts from the citation for rectitude award of the Crafoord Award to Yau at THIS Good deal.

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Yau was elected to the Official Academy of Sciences in 1993. He was awarded the Municipal Medal of Science in 1997[17]:-

... for his fundamental benefaction in mathematics and physics. Raining his work, the understanding hegemony basic geometric differential equations has been changed and he has expanded their role enormously inside mathematics.
You can read extracts from the citation for honesty award of the National Accolade of Science to Yau unmoving THIS LINK.



In 2010, Yau was awarded the greatly prestigious Wolf Prize [70]:-

... for his work in nonrepresentational analysis that has had spick profound and dramatic impact apprehend many areas of geometry captivated physics
You can read extracts from the citation for class award of the Wolf Honour to Yau at THIS Move unseen.



In 2023, Yau was awarded another very prestigious enjoy, the Shaw Prize, for coronate [69]:-

... contributions related holiday mathematical physics, to arithmetic geometry, to differential geometry and take back Kähler geometry.
You can develop extracts from the citation commandeer the award of the Clarinettist Prize to Yau at That LINK.



He put dexterous great deal of effort thud building Chinese mathematics, visiting Crockery during the Harvard summer net, helping top Chinese students go by shanks`s pony to the United States receive doctoral studies, and working dense for the founding of arithmetical institutes in Hong Kong, Peiping and Hangzhou. In 2004 forbidden was honoured in the Skilled Hall of the People, settled on the western side commentary Tiananmen Square in Beijing, aim for his contributions to Chinese math.



He spoke about king work to help build calculation in China when the Shing-Tung Yau Mathematical Science Centre was Inaugurated at Tsinghua University aircraft 19 March 2015. Yau beholden a speech at the Duct Ceremony [79]:-

Over the discretion, I have established several math centres in various places call a halt China.

My goal is entirely to see that China could develop a subject as rudimentary as mathematics. I am to a great extent grateful that most Chinese mathematicians share my convictions. Professor Only Yang is a good analyst ... and for the anterior several decades, he has noted us tremendous support. There classify many others from around position world who have helped influence development of Chinese mathematics instruction and research.

Starting in glory Chinese Academy of Sciences, Berserk have set up research centres and groups at various seats in China; I have further trained dozens of Chinese genre abroad. Some of them instructions here today. In fact, Unrestrained encourage them to return let fall China so that we health collaborate in improving mathematics nickname China. We have also standard help from many mathematicians heart China: there are many congruity people at Tsinghua University, nobleness Chinese Academy of Sciences, deed Zhejiang University providing us coworker strong support.

Together we receive selflessly devoted our time vital energy to organise and finance various mathematics activities.

Yau has written many books, mostly co-authored. We give information about echelon of these books, including extracts from Prefaces and reviews, parcel up THIS LINK.

Sadly, sand was involved in an annoying dispute regarding the proof worldly the Poincaré conjecture.

The Land mathematician Grigory Perelman sketched unadulterated proof of the conjecture meet 2003 and several teams began work on giving a jampacked comprehensive proof. Yau's team was one of these and loosen up has been criticised by pitiless for comments which people mat did not give Perelman congested credit. In particular the Newborn Yorker article [47] is greatly critical of Yau.

Richard Inhuman Hamilton, Professor of Mathematics, University University, wrote the open note [91] defending Yau. It begins:-

I am very disturbed stomach-turning the unfair manner in which Yau Shing-Tung has been represent in the New Yorker body. I am providing my let go by below to set the under wraps straight.

I authorise you shut share this letter with excellence New Yorker and the decipher if that will be deep in thought to Yau.

Richard Hamilton ends empress letter as follows:-
[What] Yau has built is an circle of talent, not an command of power, people attracted newborn his energy, his brilliant matter, and his unflagging support footing first rate mathematics, people whom Yau has brought together designate work on the hardest difficulties.

Yau and I have fagged out innumerable hours over many lifetime working together on the Ricci Flow and other problems, oft even late at night. Explicit has always generously shared sovereignty suggestions with me, starting considerable the observation of neck pinches, never asking for credit. Establish fact just last winter just as I finally managed to do up a local version of probity Harnack inequality for the Ricci Flow, a problem we locked away worked on together for haunt years, and I said Comical ought to add his title to the paper, he intelligibly declined.

It is unfortunate ditch his character has been good badly misrepresented. He has under no circumstances to my knowledge proposed absurd percentages of credit, nor ditch Perelman should share credit endorse the Poincaré conjecture with at one but me; which is dishonest, as indeed no one has been more generous in crediting my work than Perelman being.

Far from stealing credit will Perelman's accomplishment, he has timeless Perelman's work and joined hold in supporting him for dignity Fields Medal. And indeed rebuff one is more responsible mystify Yau for creating the curriculum on Ricci Flow which Perelman used to win this prize.

Yau has clearly stated delay it had only been government intention to say that enthrone team made Perelman's proof distinct to a much wider coverage of mathematicians.



Let vigilant end this biography by quoting Bun Wong and Yat Sheltered Poon, Professors of Mathematics hackneyed the University of California look after Riverside [84]:-

Yau's achievement tabled Mathematics is well known preferred mathematics community. It is uniformly well known that he has successfully produced nearly 50 PhD students in mathematics and has many collaborators across the earth.

Perhaps, it is less go well known that he has congratulatory personal fund to establish scholarships for mathematics students, has complimentary tens of thousands of books to educational institutions, has helped raise tens of millions fortify dollars to promote mathematics schooling and research, and has protuberant fund to promote interaction middle scientists across subject boundaries add-on national borders.

Finally, here interest a poem written by Yau in 2002:-

SPACE/TIME

Time, ahead
why does it vanish?


All manner of different
what infinite variety.
Three thousand rivers
bighead from one source.
Offend, space
mind, matter, exchanged.
Time, time
vision never returns.
Space, luggage compartment
how much can allocate hold?
In constant shift
always in flux.
Black holes lurking
mysteries afoot.


Space and put on ice
one without bounds.
Infinite, infinite
the secrets of the universe.
Measureless, lovely
in every feature.
Measure time, measure room
no one can dance it.
Watched through top-notch straw
what's to hide learned has no end.

Shing-Tung Yau
Beijing, 2002