Xu Yichao, 1933, 10 was born in Hangzhou, Zhejiang Province on October 7th. During War of Resistance against Japanese Aggression's period, he entered primary school, fled and studied. Zunyi junior high school, Chongqing senior high school. Chongqing junior high school 1 year. At that time, due to his poor family, he suffered from acute appendicitis and could not be treated. After half a year, appendicitis recurred. During the operation, due to severe adhesion, ether was used for general anesthesia, which affected the brain and led to memory loss. In the first grade, he entered five schools before and after War of Resistance against Japanese Aggression's victory because of illness, suspension from school and transfer. Because the teaching level of coastal middle schools was much better than that of the mainland at that time, I went to Grade One in Chongqing, Shanghai and Hangzhou for two and a half years. After that, I barely rose to the second day of junior high school. These rough childhood experiences made him develop perseverance and hard work.

Chinese name: Xu Yichao

Nationality: China.

Place of birth: Hangzhou, Zhejiang Province

Date of birth:193365438+1October 7th.

Occupation: Mathematician

Graduate School: Department of Mathematical Mechanics, Peking University, majoring in mathematics.

Main achievements: There is important pioneering work in the direction of complex homogeneous bounded domain.

Representative works: homogeneous bounded domain theory, linear algebra and matrix theory, introduction to algebra.

Personal profile

Xu Yichao, mathematician. Engaged in the theoretical research of algebraic and multiple complex variable functions. There is important pioneering work in the direction of complex homogeneous bounded domain.

Digital chronology

193310/kloc-0 was born in Hangzhou, Zhejiang on October 7th.

1952 was admitted to the Department of Mathematical Mechanics in Peking University.

1956 graduated from the department of mathematical mechanics in Peking University, majoring in mathematics.

65438-0956, assigned to the Institute of Mathematics of China Academy of Sciences as a research intern.

/kloc-in the spring of 0/957, he was admitted to the Graduate School of Mathematics of China Academy of Sciences.

196 1 Graduated from Institute of Mathematics, China Academy of Sciences.

1962- 1998 was appointed as an assistant researcher, associate researcher and researcher at the Institute of Mathematics, China Academy of Sciences.

1986 was hired as a doctoral supervisor by the National Academic Committee.

1999 Retired from the Institute of Mathematics, China Academy of Sciences.

In 2000, he was hired as a professor by the Department of Mathematics of Henan University.

1988- 1995 was elected as the director of chinese mathematical society.

1992 Member of chinese mathematical society Olympic Committee. Senior coach of China Mathematical Olympics, national coach.

Character experience

Xu Yichao settled in Hangzhou to study, mainly because his father was unemployed, his family life was difficult, and he could not afford to live and study. Xu Shi family in Hangzhou is a famous family in Qing Dynasty, with concentrated ancestral fields and traditional emphasis on reading. Xu Yizhuang was established to manage and support students studying in Hangzhou, and students' tuition and fees and basic living expenses can be collected in Yizhuang. With the support of Yizhuang, he finished junior high school in Hangzhou. After liberation, his mother went to work in Shanghai from Nanjing. He went to Shanghai with her and transferred to Ye Jing Middle School to finish high school.

Due to illness, transfer and other reasons, his grades were not good in the first year of high school. Chinese texts can't be memorized, and arithmetic problems can't be solved. However, from the second day of junior high school, his talent for mathematics gradually emerged. At that time, in algebra class, teachers often taught half a class and asked students to practice half a class. In practice, the teacher found that Xu Yichao's calculation ability is very strong, and he often asked him to calculate examples and exercises on the blackboard, which gradually cultivated his interest in mathematics. He soon found that all the problems of elementary school and grade one arithmetic can be easily solved by simultaneous equations. From grade three to senior high school, he has always met a good math teacher, and his interest in mathematics has gradually been established. His interest in mathematics stimulated his interest in physics and chemistry. Since the second day of junior high school, he has been the first in his class in science.

1952 After graduating from high school, he was admitted to the Department of Mathematical Mechanics of Peking University with excellent results. At that time, the adjustment of the departments had just ended, and the Department of Mathematical Mechanics of Peking University was composed of the main professors from Tsinghua, Peking University and yenching university, with a strong faculty. The department has arranged a strong basic course teacher for the adjusted first-year students in the department. Teaching analytic geometry, Min Sihe teaching mathematical analysis, Duan Xuefu teaching advanced algebra, Ding teaching linear algebra and Shen Keqi teaching physics. At that time, the teaching was in accordance with the syllabus of the Department of Mathematics of Moscow University. The textbooks were all translated into Russian and there were many courses. Strict, solid and generous basic training provided extremely strong support for his later research work.

Mathematics is his most interested subject. During his college years, he made full use of the good study conditions of Peking University and went all out to study. After mastering what the teacher said, I often take the initiative to go to the library to find reference books and questions to do. In order to squeeze out more time, even the nap time arranged by the school is often sacrificed. He usually doesn't talk much and doesn't like socializing very much. This personality objectively led him to devote all his thoughts to his studies. In his senior year, he applied for algebra. Under the guidance of Duan Xuefu, Nie Lingnv, Ding and other teachers, Xu Yichao's characteristic is that p> has two excellent academic papers on simple Lie algebras over field 0. One is to prove that a class of simple lie algebras becomes the direct sum of ideals of finite isomorphic simple lie algebras when extended to algebraic closed fields. The paper is published in Journal of Peking University. On the other hand, a new class of simple Lie algebras is found in algebraic closed fields. Results When it was submitted for trial, it was found that it was the same as R. Ray's doctoral thesis on Trans.Amer.Math.Soc, which had just arrived at that time, so it was not published. However, it can be seen that when Xu Yichao was in college, he already had the foundation and ability to engage in international advanced scientific research and achieved international research results.

During his college years, Xu Yichao was also influenced by his relative Mr. Bao Xu. Bao Xu asked him to strive for perfection in reading and research, to solve problems, not to be greedy and not to pursue the number of papers. These thoughts have a certain influence on his demeanor in scientific research in the future. After graduating from college, he was assigned to work in the Institute of Mathematics of China Academy of Sciences. The excellent research conditions and environment of the Institute of Mathematics have pushed his research work to a new height. 1957 applied for graduate students in the Institute of Mathematics at the beginning, and was admitted with the highest total score. The tutor is Professor Hua. When I was a graduate student, I soon met Hongbian. Xu Yichao and Chen Jingrun were designated as the white flags of the Institute of Mathematics. The result of raising the white flag is: Chen Jingrun was transferred from the School of Mathematics to the Northeast; Because Xu Yichao is a graduate student, he will handle it according to the documents of the Academy of Sciences after graduation, so he still stays in the Institute of Mathematics. 1959, Hua proposed not to take the algebra postgraduate exam, and asked Xu Yichao to become a postgraduate in complex variable function theory. Since then, his work has mainly focused on algebra of multiple complex variables. * * * Published more than 40 papers and 6 books.

school achievement

Xu Yichao mainly carried out the research work of complex homogeneous bounded domain, and obtained very rich research results, which have the international advanced level and created a new situation in the research of complex homogeneous bounded domain. The famous Riemann theorem in the theory of simple complex functions asserts that a simply connected domain with at least two points on the boundary is holomorphic and equivalent to the unit circle. This result cannot be generalized to the case of multiple complex variables. E Cartan introduces Hermite symmetric space, gives a complete classification from the perspective of homogeneous space, and proves that it is the topological product of four typical domains (which can be clearly defined in complex Euclidean space) and two exceptional indecomposable Hermite symmetric spaces (one is complex 16 dimension and the other is complex 27 dimension). Later Harish-Chandra proved that Hermite symmetric space can be completely embedded in Euclidean space and is a bounded domain (called symmetric bounded domain), but we still don't know what these two exceptions are. Because Hermite symmetric space is a homogeneous complex manifold, Cartan conjectures that any homogeneous bounded domain is holomorphic equivalent of symmetric bounded domain. Hua gave a weak conjecture: the holomorphic section curvature of any homogeneous bounded domain is always non-positive. From 1959 to 1963, Piatetski-Shapiro of the former Soviet Union denied Cartesian conjecture with two counterexamples, introduced Siegel domain, and proved that Siegel domain (unbounded domain) is holomorphic, equivalent to bounded domain, and the same as Vinberg and Titkin. In 196 1, Lu Qikeng and Xu Yichao denied the Hua conjecture with some counterexamples.

From the point of view of classification, the next problem is the classification of homogeneous Siegel fields. Xu Yichao turned this problem into an elementary matrix theory problem. Firstly, he defined a set of real matrices and complex matrices (called normal matrix sets), and introduced normal Siegel fields (homogeneous Siegel fields in complex Euclidean space) by using these matrices: Cj(z) and Qj(u) are both square matrices, and the definitions are clear. Then, he proved that any homogeneous Siegel field is linearly equivalent to the normal Siegel field, and there is holomorphic equivalence between the normal Siegel fields if and only if the normal matrix groups defining them are equivalent to each other under a special relationship. In this way, the classification problem of homogeneous bounded domains is reduced to the equivalent classification problem of normal matrix groups. Along this line of thought, he gave a complete classification under the assumption that all matrices in a normal matrix group are square matrices. These results unexpectedly include Cartan's results on Hermite symmetric space, that is, the specific expressions of the definition domains of those two exceptions are found. Xu Yichao's above achievement was made around 1965, but it was not published until 1976 because of the "four clean-ups" movement and the "Cultural Revolution" movement.

The so-called homogeneous space is a connected lie group G module and a special closed subgroup H, where G is an automorphism group on G/H, so the holomorphic automorphism group of homogeneous bounded domain is very important. Therefore, many mathematicians hope to find holomorphic automorphism groups and have done a lot of work for this purpose. This problem was independently solved by German mathematicians Dorfmaster and Xu Yichao in 1976. The former is difficult to further study the specific properties of holomorphic automorphism groups because of some characterizations of general homogeneous Siegel fields.

Using the concrete expressions of normal Siegel fields, Xu Yichao calculated their Bergman kernel functions, Bergman metrics, Cauchy-Segeg kernels and formal Poisson kernels, and proved that the necessary and sufficient condition for formal Poisson kernels to be Poisson kernels is homogeneous Siegel field symmetry. In addition, he also discussed the second-order invariant differential operator of homogeneous Siegel domain, proved that the Bergman mapping of homogeneous Siegel domain is holomorphic isomorphism, and found out why there is no way to discuss the function theory on homogeneous bounded domain with the realization of Vinberg aligning sub-Siegel domain.

The realization of Xu Yi's super-homogeneous Siegel domain greatly promotes the study of functional and geometric properties of homogeneous bounded domain, and makes the study of these problems computable. He proved that the formal Poisson kernel of asymmetric homogeneous Siegel domain is not Poisson kernel, and then proposed how to establish the theory of harmonic function on asymmetric homogeneous Siegel domain, that is, to study the properties of the solution space of Laplace-Beltrami equation. On the other hand, he gave a set of standard bases and multiplication tables of lie algebras of holomorphic automorphism groups, which provided good conditions for studying this kind of lie algebras. Xu Yichao's work is internationally recognized as the most important work in Siegel field since 1975. J.L. Koszul, a famous French mathematician, commented: "In my opinion, Xu Yichao's work on convex cones and Siegel fields is the most important and fundamental contribution to this theory since 1975, which should promote new development in many directions. Although it is necessary to better understand the algebraic structure of normal cone after introduction, as Xu Yichao's outstanding work shows, once this method is mastered, it is a very effective tool. " This work of Xu Yichao won the second prize of China Academy of Sciences 1987.

Vinberg and Titkin suspect that homogeneous Keller manifold is holomorphic fiber bundle, the bottom space is homogeneous bounded domain, and the bundle space is compact homogeneous Keller manifold. Master Dolph proved this conjecture. On the basis of Nobuyuki Murakami's work, Xu Yichao gave a complete classification of Keller manifolds under the transitivity of reduced Lie groups.

He also considered the classification in bounded domain with Thullen condition in two-dimensional complex Euclidean space. Runtu and H. Cartan gave a complete classification of Reinhardt domain, circular domain and semi-circular domain. Xu Yichao and his students gave a complete classification of semicircle domain and positive (m, p) circle domain, and provided many meaningful standard domains. This method of constructing standard domain is very useful for studying standard domain under other Thuram conditions and extending it to multiple complex variables.

From 1958 to 1976, Xu Yichao undertook many different mathematical application tasks. 1958, the Institute of Mathematics dissolved the algebra, number theory and topology groups and established the operation group. Participated in the group to promote linear planning, and participated in the programming of transportation and national grain distribution. On this basis, Xu Yichao, Wang Yuan and others compiled the Theory and Application of Linear Programming, which was published by Higher Education Press with the number 1959. This is the first book on linear programming in China. 1969, he completed the calculation task of primitive polynomials over the field of feature 2; 1976 completed the calculation task of small-scale population forecast. These works have been well received by users.

Since 1986, Xu Yichao has actively participated in the middle school students' mathematics competition. He participated in the training of the first China Mathematical Olympic Training Team, selected six players, and achieved good results in the international mathematical competition. Since 1992, I have participated in the proposition group of China Mathematical Olympiad, participated in the selection of training team members and overseas representatives, made my due contribution to China's winning the first total score and a large number of gold medals in the International Mathematical Olympiad for many years, and won honor for the motherland. 65438-0998 was hired by chinese mathematical society Olympic Committee as the national coach of Mathematical Olympiad.

Although scientific research institutions have no teaching tasks, Xu Yichao is very concerned about college mathematics education; He has taught advanced algebra 196 1 and 1963, Nankai University 1986, Tsinghua University 1989 and Henan University in 2000. Among them, the teaching time of 6 1 and 63 grades in the Department of Mathematics of the Chinese University of Science and Technology is as long as 4 years, and the teaching contents include analytic geometry of plane and space, advanced algebra, linear algebra, abstract algebra and so on. Later, he compiled the lecture notes into Introduction to Algebra, which was published in Shanghai Science and Technology Press on 1966 on the recommendation of Professor Hua. This book, for the first time in domestic textbooks, makes full use of matrix tools to turn linear space problems into algebraic problems. The book contains a large number of difficult problems, which has become a necessary reference book for graduate students after the Cultural Revolution and influenced many advanced algebra textbooks published after the Cultural Revolution. 1992, in order to meet the new needs, he rearranged some chapters in Introduction to Algebra and rewritten it into a book, Linear Algebra and Matrix Theory, which was published by Higher Education Press. The book won the first prize of 1996 National Excellent Textbook. It can be said that Introduction to Algebra, as the basic teaching material and teaching reference book of linear algebra, has fully influenced several generations.

Xu Yichao is one of the few mathematicians in China who are really familiar with Lie Qun. 1983 collaborated with Professor Yan Zhida to publish the book Lie Qun and Lie Algebra in Higher Education Press, and won the second prize of 1990 National Excellent Textbook. In 2000, he published Lie Qun and Hermite symmetric spaces in Science Press. He has taught Li Qun as a graduate student in Peking University, University of Science and Technology China, Graduate School of China Academy of Sciences, Hangzhou University, Zhengzhou University, Zhejiang University, Nankai University and Henan University, which has made indelible contributions to the popularization of Li Qun in China. Xu Yichao's lecture is clear in thinking, thorough in reasoning, inspiring and outstanding in teaching effect, which is well received by students and teachers everywhere. In the lecture, he paid special attention to explain clearly what the idea of proof was and why he thought so. He is good at analyzing the course content, paying attention to basic training, the essence of the course and the application of mathematical skills, which can lay a solid foundation for students to engage in research work in the future.

Main thesis

1 Lu Qikeng, Xu Yichao. A note on transitive domain. Journal of Mathematics, 196 1,1:1-23.

Xu Yichao, Wang Delin. Holomorphic automorphism groups on bounded positive (m, p) circular domains. Journal of Mathematics, 1963, 13: 4 19-432.

3 Xu Yichao. Automorphism groups of homogeneous bounded domains. Journal of Mathematics, 1976,19:169-19/.

4 Xu Yichao. Isomorphism of homogeneous bounded domains. Journal of Mathematics, 1977, 20: 248-266.

5 Xu Yichao. Siegel field of the first kind on a square cone. Journal of Mathematics,1978,21:1-17.

6 Xu Yichao. Classification of square fields. China Science, 1979, 22: 375-392.

7 Xu Yichao. On thebergmankernelFunction of homogeneous bounded domain. China science, 1979, special issue, Ⅱ: 80-90.

8 Xu Yichao. Anoteothhomogeneoussiegeldomains。 Actamath。 China Academy of Sciences, 198 1, 24: 99— 105.

9 Xu Yichao. Tubedomainsovercones of Dualsquaretype China Science, 198 1, 24:1475-1488.

10 Xu Yichao. On semivariogram differential operator of ordertwooverstensteinsiegaldomains Actamath。 China Academy of Sciences, 1982, 25: 340-353.

1 1 Xu Yichao. Typical realization of homogeneous bounded region. China Science, 1983, 26: 25-34.

12 Xu Yichao. Classification of aclassohomogeniouskahleriamenifolds. Clinical Science, 1986, 29: 449-463.

13 Xu Yichao. On the classification of homogeneous bounded domains. Advanced Mathematics Science in China,1988,2:105—137. Science Press: China, Peking and John Wonderly &; Son of new york.

14 Xu Yichao. There is no vertex operator of affine algebra of the first kind. Press proceedings, 1993, 280-299, World Science Press.

15 Xu Yichao. Exceptionally symmetric classical fields. Progress Science, 1999, 9: 330-339.

16 Xu Yichao. Introduction to algebra. Shanghai: Shanghai Science and Technology Press, 1966

17 Yan Zhida, Xu Yichao. Lie groups and lie algebras. Beijing: Higher Education Press, 1983.

Xu yichao Linear algebra and matrix theory. Beijing: Higher Education Press, 1992.

19 Xu Yichao. Homogeneous bounded domain theory. Beijing Science Press 2000.

20 Xu Yichao. Lie groups and Hermite symmetric spaces. Beijing: Science Press, 200 1

2 1 Xu Yichao. Bounded domain theory of complex isomorphism. k 1 uwer press &； China Science Press, 2004.