More comments on Tian's works
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More comments on Tian's works
送交者: okyautian 2005年10月06日07:01:24 于 [教育与学术]http://www.bbsla
nd.com
yautian's comments on Tian's work are fair, but here are some more inxxx
xation about these works:
The n=2 case of the KE metric of positive first Chern class was develope
d from Tian's thesis by using a trick first found by Siu. Siu gave
lectures at Columbia
and other occasions and Tian was in the audience. After that Tian wrote
up a paper which became part of his thesis. Siu was very angry, and said
that Tian had moral problem. He wrote two emotional letters to Yau aski
ng for a copy of Tian's paper. But Tian did not even show Siu the paper
before it was published in Inventiones which was very unsual. Siu publis
hed his paper in Annals of Math with remarks about the history of the wo
rk and the lectures he gave on various occasions on which Tian was in au
dience. Tian got offer from Princeton when he graduated with Yau's stron
g recommendation. But he did not get NSF grant, and after Siu told him t
he story, J. Kohn of Princeton asked Tian to withdraw the offer from Pri
nceton because he thought they made a mistake to offer him. Even now Siu
still claims that Tian's work on the n=2 case has serious gap, so incom
plete. In fact Nadel gave simple proofs of most of the n=2 cases, except
when 6 points are blown-up which may have problem.
About his work on Gromov-Witten invariants. As yautian said, Ruan needed
some
analysis to define such invariants on semipositive symplectic manfolds,
but it was known that the analysis is more or less the same as in the ga
uge theory case which Taubes had developed. In fact GW theory was an ana
logue of Gauge theory in some sense. Tian basically copied Taubes' analy
sis, but still missed some key point: Taubes only needs to consider 1 bu
bbling which is enough for gauge theory, but the more bubbling in the Gr
omov-Witten cases should be considered to define invariants. This is why
Taubes insisted on that Tian should not be considered for Veblen prize
based on his work on Gromov-Witten which he considered trivial.
Tian's work on calibrated geometry and gauge theory has been well-known
for having serious gap as Yau has beeen criticising him publicly for thi
s.
About Tian's recent work with Qing. Huisken-Yau proved existence and uni
queness
of the foliation which were enough for their applications in general rel
ativity. The extension of uniqueness on slightly larger reason was menti
oned in their paper but not important for application. Qing-Tian extende
d the region, but in their first version wrote that "the remaining chall
enge is the uniqueness, and we prove the uniqueness in this paper". So t
hey want to eat all credit of uniqueness based on not so interesing gene
ralization, this is why Yau was so angry. After Yau accused him, Qing-Ti
an revised their writing. In fact Tian did similar things before, just t
his time Yau caught him seriously.
When mentioning Fields medal, one member of the Fields selection committ
ee said that Tian was out in the first round. Note that Manin was the co
mmittee chair. This should have nothing to do with Yau. I guess it was T
ian himself created the rumor that he missed one vote from Kontsevich.
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Some comments on Tian's work by yautian
Tian's most important work is about the Kahler-Eienstein metric on the c
ompact complex manifold with positive chern class. Basiclly, he followed
Yau's idea. (please don't argue about it, I just tell a truth). Tianadm
ited in his published paper that it was Yau introduced him into this fie
ld and shared with him the important idea that the existence of the K-E
metric should relate to some stability in algebraic geometry. After more
than 10 years, Tian got some important results, (including the solution
for the n=2 case which brought him Waterman prize). But, the most impor
tant equivalence between the existence and stability still COMPLETELY OP
EN. Tian's lastest contribution to this problem was 1996, 9 years have p
ast.
The second important work of Tian Gang is about Gromov-Witten. Basically
, there are two approches to this problem. One is algebraic geometry, st
arted by Manin-Kontesevic. the other way is differential geometry, start
ed by Ruan,YongBin. Ruan already realized there was away to define invar
iant, and wrote one paper. But Ruan is not good at analysis, he asked Ti
an for help. This was the famous Ruan-Tian paper published on 1995 JDG.
After that Tian continued to do important work on Gromov-Witten theory.
This time, his collaborator was Li Jun, who is a famous algebraic geomet
er. Their theory was called "Li-Tian's work. It is not was Tian's single
work. Their collaboration was 50%-50%, nobody played the dominent role.
After that, Tian never dis Grmov-Witten theory again.But Li Jun write 2
very important long papers, made a fundamental contribution to the algeb
raic-geometry understanding of Gromov-Witten theory.
Tian's third important work was his 2000 annals paper--gauge theory and
calibrated geometry. But this worked was inspired by Donaldson-Thomas th
eory, and borrowed heavilly analysis technique from Fanghua Lin's 2001 a
nnals paper about harmonic map.
"No works initiaed from Tian, no work ended by Tian". It is a correct cp
mment.
Tian definitely is a first-rate geometer, but definitely not a super rat
ed. It is quite fair to him not awarded Fields medal.
I don't agree that Tian steal other's work. In this point, I don't agree
with Yau. I know which paper Yau mentioned. Tian and Qin Jie generalize
d some work of Yau-Huisken. I admit that it is not a very important gene
ranization. But not steal. The point, as a famous geometer, Tian needn't
write such a not-high quality paper.
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