2024-08-01
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The number theory and algebra award jointly sponsored by the Institute of Mathematics and Systems Science of the Chinese Academy of SciencesThe First Chen Jingrun AwardRevealed!
A total of two research results won awards.
One is a post-90s professor from the Institute of Data Science at Shandong UniversityHuang BingrongHis award-winning achievements are:
Moments of L-functions and their applications to the Rankin-Selberg problem and arithmetic quantum chaos.
△Professor Dorian Goldfeld and Academician Xi Nanhua presented the award to Huang Bingrong. Image source: Official website of the Institute of Mathematics and Systems Science, Chinese Academy of Sciences
Another winner is a researcher from the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences in 1984.Nie SianThe winning results are:
Irreducible bifurcations of affine Deligne-Lusztig varieties.
△ Professor Zhang Shouwu and Academician Zhang Ping presented the award to Nie Sian. Image source: Official website of the Institute of Mathematics and Systems Science, Chinese Academy of Sciences
The Chen Jingrun Award is sponsored by the Chinese Academy of Sciences Institute of Mathematics and Systems Science and the Chinese Academy of Sciences University Education Foundation.Commemorate the contributions of Mr. Chen Jingrun, a famous Chinese number theorist, and promote his spirit of struggle in spite of difficulties and his love for mathematics" was established.
Aims to reward and recognize the number theory and algebra projects completed in ChinaUnder 40 years oldOutstanding achievements of young talents.
The award is given every two years, with a maximum of two winning achievements each time. This is the first time the award has been given. Each achievement will receive a prize of 200,000 yuan, and a certificate will also be issued.
It is worth mentioning that this awardThe main purpose is to discover new people, and no longer reward relevant implementers who have won major domestic or international awards.
Huang Bingrong, born in 1990, is currently a professor and doctoral supervisor at the Institute of Data Science, Shandong University.
From September 2012 to June 2017, he studied for a doctorate degree at the School of Mathematics of Shandong University. His supervisor was 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 at Columbia University in the United States as a joint doctoral student, with Professor Dorian Goldfeld as his supervisor.
From October 2017 to August 2019, he worked as a postdoctoral fellow at the School of Mathematical Sciences, Tel Aviv University, Israel, with Professor Zeév Rudnick as his supervisor.
Before winning the Chen Jingrun Award, Huang Bingrong was an outstanding young and middle-aged scholar at Shandong University, selected into the national youth talent program and a young expert of Shandong Province Taishan Scholars.
The official website describes his award-winning research results as follows:
L-functions, including the Riemann zeta function, are one of the main research objects in analytic number theory. The estimation of L-function moments is a core problem in number theory and has important applications in fields such as automorphic forms and quantum chaos.
The Rankin-Selberg problem aims to improve the remainder of the quadratic mean of the Fourier coefficients of the automorphic form proved by Rankin and Selberg in 1939/1940.First breakthroughThe core of the proof is to transform the problem into the moment of L-function and relate it to the subconvex bound problem of third-order L-function, so as to solve the problem using the delta method.
Arithmetic quantum chaos studies chaotic systems with arithmetic structures, and arithmetic hyperboloids are one of the main models. The characteristic function of the Laplace operator, namely the Maass form, and its value distribution in the semiclassical limit are one of the main research issues, including the random wave conjecture and the quantum wave conjecture. This result uses the estimation of the L-function moment,Solved the third-order moment problem of the Hecke-Maass form and the quantum variance problem of the Eisenstein seriesCompared with quantum unique ergodicity (i.e., second-order moment), this result obtains a quantized upper bound for the third-order moment.
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 observable matrix. In the general case of chaos, there are conjectures in the physics literature that relate this quantum variance to the autocorrelations of the observables along the classical motion. These conjectures have not been proven in most cases.
Huang Bingrong's research results studied the quantum variance of the continuous spectrum in the modular domain. Specifically, he studied:
Quantum variance of the Eisenstein series on .
His research proved an asymptotic formula for the quantum variance of Eisenstein series, compared the results with classical variance and quantum variance of cusp form, and found that these variances are consistent after plugging in certain subtle arithmetic factors (including the central values of certain L-functions).
This provides a new computable instance of quantum variance in quantum chaos theory, helping to understand the relationship between quantum and classical systems.
Nie Sian, born in 1984, is currently a researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
He graduated from the Zhu Kezhen College of Zhejiang University in 2007 and received his Ph.D. in Science from the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences in 2012, with his supervisor being Academician Xi Nanhua.
He has conducted postdoctoral research at the Institut des Hautes Études Scientifiques (IHES) in France, the Max Planck Institute for Mathematics in Germany, and the Mittag-Leffler Institute in Sweden.
His research interests include algebraic groups, affine Hecke algebras and their representation theory, the geometry of affine Deligne-Lusztig varieties and their applications in arithmetic geometry.
The Chen Jingrun Award official website introduces its award-winning research results as follows:
Affine Deligne-Lusztig varieties are group-theoretic models of reduced Shimura varieties, and play an important role in arithmetic geometry and the Langlands program. The classification problem of irreducible branches of affine Deligne-Lusztig varieties is a fundamental open problem, and has key applications in important topics such as the Tate conjecture on Shimura varieties.
To solve this problem, Chen Miaofen and Zhu Xinwen proposed a famous conjecture: there is a canonical one-to-one correspondence between the set of orbitals of irreducible branches and the crystal basis of the specific weight space of Weyl modules.
By constructing a crystal structure on an irreducible branch, this work provides a complete proof of the Chen-Zhu conjecture and obtains a combinatorial algorithm for calculating the stable subgroups of irreducible branches.In principle, the classification problem of irreducible branches is solved。
The main paper related to the award-winning results is "IRREDUCIBLE COMPONENTS OF AFFINE DELIGNE-LUSZTIG VARIETIES", which is 62 pages long.
Here is a brief summary from AI.
The main goal of the paper is to completely solve the parameterization problem of the top-dimensional irreducible components of affine Deligne-Lusztig clusters, and three main results are proposed:
Firstly, the Chen-Zhu conjecture is proved, and a natural bijection between the set of top-dimensional irreducible components and some Mirković-Vilonen cycles is given;
Secondly, we prove that the parameterized mapping is compatible with the tensor structure, which provides a representation-theoretic approach for constructing irreducible components.
Third, in the basic case, an explicit construction of the irreducible components in each orbital is given, and its stabilizers are calculated.
The author also discusses some important consequences of these results, including the determination that the stabilizer of the irreducible component is the parabolic subgroup of maximum volume. Finally, the strategy for proving these results is outlined, reducing the problem to several key cases and applying techniques such as the semimodule method and the Littelmann path model.
This work provides deep insights into the structure of affine Deligne-Lusztig clusters.
As mentioned at the beginning, the Chen Jingrun Award was established by the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences and the Education Foundation of the University of Chinese Academy of Sciences to "commemorate Chen Jingrun's contributions and promote his spirit of fearlessness of difficulties and love of mathematics."
Chen Jingrun is a famous Chinese number theorist. In 1957, Chen Jingrun began to intern at the Institute of Mathematics of the Chinese Academy of Sciences. In 1980, he was elected as a member of the Chinese Academy of Sciences (Academician).
△Image source: Scientist story column of the Institute of Mathematics and Systems Science, Chinese Academy of Sciences
His most famous achievements include proving thatEvery sufficiently large even number can be expressed as the sum of a prime number and an integer whose prime factors do not exceed 2.”, which is a major contribution to the Goldbach conjecture.
In 1973, he published a detailed proof in Science China and improved the numerical results announced in Science Bulletin in 1966, which caused a sensation internationally. His results were called"Chen's Theorem", he still holds the world record and leading position in the research field of Goldbach's conjecture.
On the official website of the Chen Jingrun Award, a special section has been set up for Chen Jingrun, which records the life experience of the above-mentioned Chen Jingrun and his many research results.
The specific organization of the Chen Jingrun Award ceremony is undertaken by the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences. The award is presented at the academic conference on number theory and algebra organized by the Institute of Mathematics and Systems Science of the Chinese Academy of Sciences. The prize money is provided by the Education Foundation of the University of Chinese Academy of Sciences.
The chairman of the first "Chen Jingrun Award" jury was Zhang Shouwu, a member of the American Academy of Arts and Sciences and 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. In the future, he will inherit Mr. Chen Jingrun's spirit of not fearing difficulties and loving mathematics, and contribute to the development of Chinese mathematics.
Nie Sian also said that Mr. Chen Jingrun’s academic achievements still shine today, and his scientific spirit still inspires the younger generation of scientific researchers to forge ahead.
Official website of Chen Jingrun Prize: http://www.amss.ac.cn/Chen_Jing_Run_Prize/?lang=en
Paper link:
[1]https://arxiv.org/pdf/1811.02925
[2]https://arxiv.org/pdf/1809.03683
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