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The 1st Chen Jingrun Award for Number Theory and Algebra co-sponsored by the Academy of Mathematics and Systems Science, Chinese Academy of Sciences has been announced!
A total of two research results were awarded.
One is Huang Bingrong, a post-90s professor from the Institute of Data Science of Shandong University, whose award-winning achievements are:
The moment of the L-function and its application to the Rankin-Selberg problem and arithmetic quantum chaos.
△Professor Dorian Goldfeld and Academician Xi Nanhua presented the award to Huang Bingrong, source: official website of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Another winner is Nie Si'an, an 84-year researcher at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences, and the award-winning results are:
仿射Deligne-lusztig簇的不可约分支。
△Professor Zhang Shouwu and Academician Zhang Ping presented the award to Nie Si'an, source: official website of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences
The Chen Jingrun Award was established by the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences and the University of Chinese Academy of Sciences Education Foundation to "commemorate the contribution of Mr. Chen Jingrun, a famous Chinese number theorist, and promote his fighting spirit of defying difficulties and loving mathematics".
It aims to reward and recognize the outstanding achievements of young talents under the age of 40 in the direction of number theory and algebra completed in China.
This is the first time that the award is presented every two years, with a maximum of two winners at a time. The prize money for each achievement is 200,000 yuan, and the award certificate will be issued at the same time.
It is worth mentioning that the main purpose of this award is to discover new people, and it will no longer reward relevant finishers who have won major awards at home and abroad.
Post-90s professor of Shanda University, grandson of Pan Chengdong
Huang Bingrong, born in 1990, is currently a professor and doctoral supervisor of the Institute of Data Science of Shandong University.
From September 2012 to June 2017, he studied for a Ph.D. in the School of Mathematics of Shandong University, under the supervision of Professor Liu Jianya, who is currently the vice president of Shandong University and a disciple of the famous Chinese mathematician Pan Chengdong.
In addition, from August 2015 to February 2017, Huang Bingrong went to the Department of Mathematics of United States Colombia University as a joint doctoral student, under the supervision of Professor Dorian Goldfeld.
From October 2017 to August 2019, he worked as a postdoctoral fellow at the School of Mathematical Sciences, Tel Aviv University, Israel, under the supervision of Prof. Zeév Rudnick.
Prior to winning the Chen Jingrun Award, Huang Bingrong was also an outstanding young and middle-aged scholar at Shandong University, and was selected into the National Young Talent Program and Shandong Taishan Scholar Young Expert.
For his award-winning research results, the official website is:
L-functions, including Riemann ζ functions, are one of the main research objects of analytic number theory. The estimation of L-function moments is the core problem of number theory, and has important applications in the fields of self-defending forms and quantum chaos.
The Rankin-Selberg problem aims to improve the remainder of the quadratic mean of the Fourier coefficient of the self-defending form demonstrated by Rankin and Selberg in 1939/1940. This achievement broke through this long-standing barrier for the first time in 2021 and obtained a subconvexity index. The core of the proof is to transform the problem into the moment of the L-function and associate it with the subconvex boundary problem of the third-order L-function, so as to solve the problem by using the delta method.
Arithmetic quantum chaos studies chaotic systems with arithmetic structures, and arithmetic hyperboloids are one of the main models. The value distribution of the eigenfunction of the Laplace operator, i.e., the Maass form, at the semi-classical limit is one of the main research problems, including the random wave conjecture and the quantum wave conjecture. In this paper, the third-order moment problem of Hecke-Maass form and the quantum variance problem of Eisenstein series are solved by using the estimation of L-function moments. Compared with the quantum-unique ergodic (i.e., the second-order moment), the quantized upper bound of the third-order moment is obtained.
We used AI to help summarize the first award-winning paper.
An important problem in quantum chaos theory is to understand the variance of the coefficients of the observably measured matrices. In the general chaotic case, there are conjectures in the physics literature that link this quantum variance to the autocorrelation of observable measurements along classical motion. For the most part, these conjectures have not been proven.
Wong's research results include the study of quantum variance on a continuum of modular domains, specifically:
quantum variance on the Eisenstein series.
His work proved the asymptotic formula for the subvariance of the Eisenstein order of quantity, comparing the results with the classical variance and the quantum variance in the pointed form, and found that these variances were consistent after inserting certain subtle arithmetic factors, including the central values of certain L-functions.
This provides a new computable example of quantum variance for quantum chaos theory, which helps to understand the relationship between quantum and classical systems.
Solve the problem of irreducible branch classification
Nie Si'an, born in 1984, is currently a researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
He graduated from Zhu Kezhen College of Zhejiang University with a bachelor's degree in 2007 and received a Ph.D. degree from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2012.
He has conducted postdoctoral research at the Institut des Hautes Etudes des Sciences (IHES) in France, the Max Planck Institute of Mathematics in Germany, and the Mittag-Leffler Institute in Sweden.
His research interests include algebraic groups, affine Hecke algebra and its representation theory, and the geometry of affine Deligne-Lusztig clusters and their applications in arithmetic geometry.
The official website of the Chen Jingrun Award introduces the award-winning research results:
The affine Deligne-Lusztig cluster is a reduced group theory model of the Shimura cluster, which plays an important role in arithmetic geometry and the Langlands program. The classification problem of the irreducible branches of affine Deligne-Lusztig clusters is a basic public problem, and it has a key application in important topics such as the Tate conjecture on the Shimura cluster.
In order to solve this problem, Chen Miaofen and Zhu Xinwen put forward a famous conjecture: there is a one-to-one correspondence between the irreducible branch orbital set and the crystal base of the specific weight space of the Weyl mode.
By constructing the crystal structure on the irreducible branches, the complete proof of the Chen-Zhu conjecture is given, and a combinatorial algorithm for calculating the stable subgroups of the irreducible branches is obtained, which solves the classification problem of the irreducible branches in principle.
获奖成果相关主要论著为“IRREDUCIBLE COMPONENTS OF AFFINE DELIGNE-LUSZTIG VARIETIES”，论文长达62页。
Here's a quick summary from AI.
The main goal of this paper is to completely solve the parameterization problem of the irreducible components of the apex dimension of affine Deligne-Lusztig clusters, and three main results are proposed:
Firstly, the Chen-Zhu conjecture is proved, and the natural biprojection between the set of irreducible components of the top dimension and some Mirković-Vilonen cycles is given.
Secondly, it is proved that the parametric mapping is compatible with tensor structures, which provides a representational method for constructing irreducible components.
Thirdly, in the basic case, the explicit constructs of the irreducible components in each orbital are given, and their stabilizers are calculated.
The authors also discuss some important corollaries of these results, including the determination that irreducible stabilizers are the largest volume of parabolic subgroups. Finally, the strategies to prove these results are outlined, the problem is reduced to several key cases, and techniques such as the half-mode method and the Littelmann path model are applied.
This work provides insight into the structure of affine Deligne-Lusztig clusters.
The first Chen Jingrun Award
As mentioned at the beginning, the Chen Jingrun Award was established by the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences and the University of Chinese Academy of Sciences Education Foundation to "commemorate Chen Jingrun's contributions and promote his fighting spirit of defying difficulties and loving mathematics".
Chen Jingrun is a famous number theorist in China, since 1957, Chen Jingrun entered the Institute of Mathematics of the Chinese Academy of Sciences as an intern, and was elected as a member (academician) of the Chinese Academy of Sciences in 1980.
△ Source: Scientist story column of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences
His most famous achievements include proving that "every sufficiently large even number can be expressed as the sum of a prime number and an integer with no more than two prime factors", which was a major contribution to Goldbach's conjecture.
In 1973, he published a detailed proof and improvement of the numerical results announced in Science Bulletin in 1966 in Science China, which caused an international sensation, and the result was called "Chen's theorem", and he still holds the world record and leading position in the field of Goldbach conjecture research.
On the official website of the Chen Jingrun Award, the official has set up a special topic on Chen Jingrun, which records the life experience of Chen Jingrun and many of his research achievements mentioned above.
The Chen Jingrun Prize was awarded at the Academic Conference on Number Theory and Algebra organized by the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and the prize money was provided by the University Education Foundation of the Chinese Academy of Sciences.
The director of the first "Chen Jingrun Award" award committee is Zhang Shouwu, a member of the United States Academy of Arts and Sciences and a professor at Princeton University.
According to China Youth Daily, Huang Bingrong said in his acceptance speech that he was grateful to his mentor for leading him into the world of analytic number theory, and that in the future, he will inherit Mr. Chen Jingrun's fighting spirit of defying difficulties and loving mathematics, and contribute to the development of Chinese mathematics.
Nie Si'an also said that Mr. Chen Jingrun's academic achievements still shine today, and his scientific spirit still inspires the younger generation of researchers to forge ahead.
Chen Jingrun Award official website: http://www.amss.ac.cn/Chen_Jing_Run_Prize/?lang=en
Paper Links:
[1]https://arxiv.org/pdf/1811.02925
[2]https://arxiv.org/pdf/1809.03683
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