Response to the Letters

Transcription

1 Response to the Letters Zhuang-dan Guan November 4, 2006 The Dean office has asked me to say some thing about the six outside references I chose for my Career Review case. First, I like to explain that I chose them because of two reasons: A. They are the most knowledgible people of me and of some of my work. B. There are seemly not conflict of interest between me and them as one of the outside reviewers said that I have many enemies at least those people think in that way. I will give some records about my relation with the outside reviewers I chose in the item 1 to 6. In the item 7 to 12, I will explain some related issues. 1. I met professor Dorfmeister in After the death of my master advicer Zhong, J. Q. Professor Wang, Q. M. (since a byproduct of my first paper answered a question which professor Wang gave to his student) introduced me to him. Professor Dorfmeister was one of the leading figure in the study of Kähler homogeneous spaces. After a long cumulative work he finished the proof of the Fundamental Conjecture of Kähler homogeneous spaces. This is a good success in mathematics as a mathematician. He was interesting in my first paper and another unpublished work (see his review of MR 88m: 32062). I was a student of him for a year before he left for another university because of a promotion issue. Now he is in Technic University of München in Germany, which is recently picked up by the Germany government as the first of three top universities. It is in the eight place in the list of European universities in htm. You could easily see the influence of that year on my mathematics work through my publications on homogeneous spaces and almost homogeneous manifolds. And my preparations in these areas eventually lead to the final breakthrough on the geodesic stability and the existence of extremal metrics on compact almost homogeneous manifolds of cohomogeneity one. 1

2 2. Professor Huckleberry is very like a king in the area of complex homogeneous spaces and almost homogeneous spaces (as one of the outside reviewer said) just as professor Yau is very like an emperor in the Calabi-Yau area. When we tried to publish our result on the classification of compact pseudo-kähler homogeneous space, he gave a different proof and that eventually lead me to a lot of best results in this field. Three years ago, he wrote in the reference to my tenure case that my work was enough for a full professor here. 3. In our paper on compact pseudo-kähler homogeneous space we used a result of professor Kobayashi which also lead me to one of the best result on the compact homogeneous space. This later result was mentioned by professor Wolf in his letter. Professor Kobayashi is one of leading expert in the complex geometry. He has 1576 citations, which is higher than some of the Fields Medal winners, e.g., Kodaira, Hironaka, Mori. His work on Hermitian vector bundles started so call Hitchin-Kobayashi correspondence. Hitchin told Donaldson about the conjecture, which eventually lead Donaldson to the Fields Medal. The vector bundle case could be regard an example to the manifold case. That eventually lead me to post the geodesic principles and solved the Kähler-Einstein metrics problem for compact almost homogeneous manifolds of cohomogeneity one. These are some of the reasons that I got in Berkeley and became a student of Kobayashi after professor Dorfmeister s leave. One of his earlier student also worked on quaterion and hyperkähler manifolds. Professor Kobayashi had a heart attack in the early August and just recovered. 4. About the same time as we finished the compact pseudo-kählerian case we also finished the case in which the group is reductive. Actually, we proved that the space is almost the same as Wolf space. This result impressed professor Wolf as you can see from his letter. Professor Wolf is one of the best students of famous mathematics professor Chern, S. S. (who was also the professor of Yau) as I know only two of his students could stay in Berkeley. Professor Wolf is a leading figure in the representation theory of Lie group. 5. I met professor Bogomolov when professor Gromov heared about my work on compact simply connected nonkähler holomorphic symplectic manifolds and invited me to University of Maryland. At that time, professor Todorov claimed that every simply connected compact holomorphic symplectic manifold is kähler. After 10 years, none could say his proof is correct or not. After hearing a talk of professor Todorov in Berkeley, motivated by my work on homogeneous spaces I thought that I could make up at least 2

3 some non-simply connected non-kähler ones. That was how I started, but I ended up with the first compact simply connected non-kähler ones. This is unexpected for him. I eventually send it to the Inventionae. But professor Todorov and the referee could not understand my proof. First, they said, you are wrong; then, if you are right, where did I get wrong? I eventually confronted professor Todorov in Beijing in the summer 1994 and he admitted his mistakes. Then he and the referee said: ok, I am wrong, you are wrong also; then now, I am wrong, you are wrong also, but I could make up my own counter-example; lastly, your English is bad! Professor Gromov introduced me to professor Bogomolov. Professor Bogomolov is a leading figure in hyperkähler manifolds, algebraic geometry and number theory. At that time professor Todorov was in Harvard with professor Yau and I was in Princeton, alone. I really did not know what was going on in Harvard. My proof used the calculation of nilponent Lie algebra, actually very simple ones. But people who worked on this area are not at all familiar with nilponent Lie algebra. According to their curiosity, I make up the second proof by exchanging the steps. That made the things a little bit simpler. I actually gave another proof in another paper, which also avoid the symplectic reductions. All my three proofs use extensively the nilponent Lie algebra calculations. Eventually, professor Bogomolov came up a more topological proof. But he had a difficulty with the fundamental groups. I then explained to him of the choice of the special kind of Kodaira-Thurston surface. Then he published a paper in Amer. J. of Math.. People seems have confusion on everything. That is why there are several versions on this matter. This eventually lead me to consider the Hilbert construction of the first cohomogeneity one manifold with a semisimple automorphism group. People took this more serious. But for me, this is only a step toward the solving of the Calabi problem. Professor Bogomolov is also a leading figure in stability. His work on stability sparked Professor Kobayashi s work on the relation between Hermitian Einstein metrics and polystabilities. 6. When professor Gromov talked to me, he also showed me a paper of Professor Salamon and asked me whether one could get any bounds on the Betti numbers. That was in Five years later, using his result I was able to get very good bounds for the complex dimension four cases. One paper published in Math. Res. Letters. Professor Hitchin was one of the referee. In the chair letter 2001 professor Schultz said that the editor was Kobayashi. This was a mistake. Professor Yau was the editor. I eventually met professor Salamon twice in Europe, first in Durham England 2001, and then in Pisa Italy In the Dean s letter 2005, Professor Angle said that 3

4 I did not have any outside invited talk. that was another mistake. Professor Salamon is a leading figure on special holonomy geometry. He has wrote a famous book Riemannian Geometry and Holonomy Group. He was in Imperial College of London, which is at the third place in the list of the European universities we mentioned above, three years ago when he wrote a letter for me before he went to Turin. 7. When I was searching my papers for my Career Review. I incidently found an from Professor Ziv Ran to Professor Schultz. Regarding his as a sort of letter, I have to response. In that , he said that he did not read my recommendations letters, but related my work to those of Siu, Yau, Mok, Tian, and Mori on the classification of the projective manifolds. That was a totally mistake. First, my work is quite different from Siu, Yau, Mok, Tian s work on classification of projective manifolds if there is any. Second, I did some classification of Fano manifolds or some thing similar only for the purpose to find extremal metrics for the most difficult part of Calabi s question, which is quite different from that of Mori s. On the other hand, my method to classify the Fano manifolds is also algebraic, i.e., a method came out of Mori s. 8. There are some evaluations of my 10A, 10B, 131, 138A, 138B classes in in my files. 9 My laptop was stolen from my office one day after the faculty meeting of my tenure case before the Thanksgiving I used my laptop to teach in my 9A class. My class was at 12:10. I went to Commons to buy my lunch. After I bought my lunch, I could not find my laptop anymore. I was so overwhelmed that I was not able to teach. The door was still locked. Fortunately, I just graded the midterm. I could only give the midterm back to them and said happy Thanksgiving. After I told vice provost Dr. Lord, she adviced me to change the lock. However, after changing my lock, my 151C note was taken from my office in a few days. 10. In winter 2006, professor Chalmers did not finshed his part almost a chapter as what he did in 210A. Professor Schultz used a difficult textbook for 138A, but he did not follow the textbook. Therefore, in 138B I have to used his textbook and covered the part he did not finished. These caused some troubles in those classes. 11. In the chair s letter Professor Schultz said that one of my paper published in Math. Res. Letters could be accepted only because professor Kobayashi was the editor. This was a mistake. Professor Yau was the editor and Hitchin was one of the referee. See both letters from Hitchin this year and that for my tenure case. 4

5 12. In the Dean s letter for the last merit. The Dean said that I did not give any talk outside Riverside. This was a mistake. He also said that I did not apply for an NSF grant. That was not true. I was applying for an NSF grant last year. It was pending until Oct that I had to reapply. This is part of the reasons that I am doing my Career Review now. 5