本期报告具体信息如下：

时间：2022年10月22日 10:00—11:00

10:00-11:00 a.m.

October 22st, Saturday

Lecture 5            Mathematics Inspired by Physics

物理激发的数学

刘克峰

Speaker Bio

Professor Kefeng Liu is an internationally famous mathematician. He is currently professor of mathematics at University of California, Los Angeles, and the director of the Mathematical Science Research Center of Chongqing University of Technology. He is editor-in-chief of the top mathematical journal “Communications of Analysis and Geometry”. He received his PhD from Harvard University in 1993 under the supervision of S.-T. Yau. Liu has made first class contributions to differential geometry, topology and mathematical physics, he has published more than 180 papers in top mathematical journals. He was an invited speaker of the 2002 International Congress of Mathematicians, has received the Morningside Gold Medal of Mathematics which is the highest honor of Chinese descendants in mathematics, and  was rewarded the 2004 top 10 scientific advances of the Education Ministry of China, the famous Guggenheim fellowship, the Sloan fellowship and the Terman fellowship.

刘克峰教授，国际著名数学家，美国加州大学洛杉矶分校数学系教授，重庆理工大学数学中心主任，国际顶尖数学杂志Communications in Analysis and Geometry(《几何与分析通讯》)主编。1993年获美国哈佛大学数学系博士学位，师从丘成桐教授。刘教授在微分几何、拓扑、数学物理等研究方向取得了大量国际一流的原始创新成就，先后在国际一流期刊上发表学术论文180余篇，并在2002年国际数学家大会上被邀请作45分钟报告。他曾荣获全球华人数学最高奖“晨兴数学金奖”和2004年国家教育部十大科技进展，以及国际上著名的谷庚海默奖、斯隆(Sloan)奖、特曼(Terman)奖等。

Abstract

Based on my own experience I will present the exciting interactions and developments of mathematics and physics, in particular string theory. The grand unification theory in physics produced many remarkable mathematical problems and many new original ideas which stimulated the development and grand unification of mathematics. On the other hand, the solutions of these problems in mathematics perfectly verify the new theories of physics.

我将从我个人的学习和研究经历出发，介绍数学与理论物理，特别是超弦理论的交融发展。物理的大统一理论提出的许多惊人的数学问题和崭新的想法有力地推动了数学本身的发展和统一。而这些问题在数学上的解决也完美地验证了新的物理理论。

10:00-11:00 a.m.

October 23st, Sunday

Lecture 6  The Riemann Hypothesis via the generalized von Mangoldt function

黎曼猜想与广义von Mangoldt函数

William Banks

Speaker Bio

William Banks received Bachelor’s degree in California Institute of Technology under Tom M. Apostol from 1982 to 1986, Ph.D degree in Stanford University under Daniel Bump from 1989 to 1994. Prof. Banks worked in University of Carlifornia-Berkeley, Oklahoma State University and became a full professor in University of Missouri-Columbia in 2007. Prof. Banks’ research interest is in analytic number theory, algebraic number theory, representation theory and croptography. Prof. Banks has 120 publications, including Duke Math. J., J. Reine Angew. Math., Compositio Math., Trans. Amer. Math. Soc., Proc. Lond. Math.Soc.

William Banks教授于1982-1986年在加州理工学院取得学士学位，本科导师为Tom M. Apostol教授，1989-1994年在斯坦福大学师从Daniel Bump教授取得博士学位，期间先后在加州大学伯克利分校的MSRI研究所、俄克拉荷马州立大学等地工作，2007年至今任密苏里大学哥伦比亚分校正教授。William Banks教授的研究方向为解析数论、代数数论、表示论和密码学，目前已在Duke Math. J., J. Reine Angew. Math., Compositio Math., Trans. Amer. Math. Soc., Proc. Lond. Math.Soc.等杂志发表论文120篇。

Abstract

Gonek, Graham, and Lee have recently shown that the Riemann Hypothesis can be reformulated in terms of certain asymptotic estimates for twisted sums with von Mangoldt function          . Building on their ideas, for each          , Saloni Sinha and I have studied twisted sums with the generalized von Mangoldt function

and show that the Riemann Hypothesis is equivalent to the following assertion. For every       , the estimate

holds uniformly for all                        . A similar result is obtained for the function      ,

the          -fold convolution of the von Mangoldt function.

Gonek，Graham和Lee 近期证明黎曼猜想可以被描述为一类von Mangoldt函数的求和问题。以此启发，对于任意     ，我和Soloni Sinha一起研究了广义von Mangoldt函数

并证明黎曼猜想等价于以下命题：

对于任意     ，

对于任意          ,        一致成立。