报告题目：The Beurling-Kozlov-Wintner completeness problem

报告摘要：This talk concerns a long-standing problem raised by Beurling and Wintner on completeness of the dilation system generated by the odd periodic functions on the real numbers. Up to now there has been no explicit description of solutions of the Beurling-Wintner problem, even for characteristic functions. Focusing on the union of finitely many intervals with rational endpoints and using substantially techniques from analytic number theory, we fully solved the Beurling-Wintner problem in most interesting situations and exhibit the explicit form of such sets. As a consequence, it yields a  complete solutions for the rational version of Kozlov's problem.  Moreover, we find that the rational version of Kozlov's problem is closely related to the Twin Prime Problem and the Sophie Germain Prime Problem.

报告人简介：郭坤宇，复旦大学特聘教授和上海数学中心谷超豪研究所长聘教授。现任第十四届全国政协委员、复旦大学校务委员会委员、校学术委员会委员、复旦大学数学博士后流动站站长。曾任复旦大学数学科学学院院长、非线性数学模型与方法教育部重点实验室主任。2005年获国家杰出青年科学基金、2006年被聘为教育部长江学者特聘教授。先后两次获上海市自然科学奖一等奖（均为第一完成人）。长期从事基础数学的教学和科研工作，在国际知名数学期刊发表论文100多篇; 专著3部。 发展的思想、方法被学界同行称为 “郭方法”； “郭引理”；“郭-稳定性”； “郭-王定理”；“郭-王恒等式”等。 解决了算子理论中多个困难的问题，形成了复旦大学算子理论研究特色，国际同行称为“复旦学派”。

报告时间：2025年9月22日16:00-17:00

报告地点：武之楼412会议室