Academic Report of School of Mathematical Sciences [2025] No. 156

(Series Report for High-Level University Construction No. 1257)

Title：Ternary Quadratic Forms and Quasi-Primes

Speaker：Jiamin Li (Shandong University)

Time：16:00-17:00, Dec.16, 2025

Location：Room 2433, Huiwen Building

Abstract：The distribution of prime numbers ranks among the oldest problems in mathematics. Since the 20th century, analytic number theory has developed powerful tools such as sieve methods and circle methods, enabling approximations to the Goldbach conjecture, the twin prime conjecture, and even nonlinear problems like the Wallin-Goldbach conjecture through results on “quasi-primes.” About a decade ago, Bourgain, Gamburd, and Sarnak proposed a programmatic conjecture framing the prime number distribution problem within the context of group actions, opening entirely new avenues for research. This talk will focus on recent progress in quasi-prime number distribution problems associated with ternary quadratic forms. We will explore how this approach differs from the traditional framework of the Waring-Goldbach problem and demonstrate how contemporary automorphic forms theory is applied to such classical problems of prime distribution.

Speaker Profile：Jiamin Li is a 2023 doctoral candidate at the National Center for High-Level Talent Cultivation in Mathematics, Shandong University. His research focuses on analytic number theory, particularly various forms of prime number distribution problems, especially the Goldbach and twin prime conjectures. Currently leads the National Natural Science Foundation of China Young Student Basic Research Project titled “Elevation of the Degree of Prime Number Distribution and Its Applications.” Research achievements focus on exponential sums and sieving methods in analytic number theory, with four SCI-indexed papers published in high-impact journals including Science China Mathematics and Journal of Number Theory.

Faculty and students are welcome to attend!

Invited by: Yingnan Wang  

School of Mathematical Sciences

December 15, 2025