报告人：谢之福 (美国南密西西比大学)
时间：2023年06月16日 15:00-16:00
地点：beat365中文官方网站会议室80602
题目：关于平面四体问题中凸中心构型的唯一性问题
Abstract: A central configuration is a specific arrangement of masses, and a planar central configuration can lead to a homographic periodic solution. It is crucial for understanding the dynamic behavior of the N-body problem, and the question of its finiteness has been a challenge for mathematicians in the 21st century. For the planar four-body problem, its finiteness has been proven by computer-assisted proof in 2006 by Hampton and Moeckel, but there is still much to understand. One conjecture is that there exists a unique convex central configuration for any four positive masses in a given order. Many research paper has attempted this question by assuming either having some equal masses or having restrictions of the geometric shape such as a trapezoid or co-circular shape. In this talk, we provide a rigorous computer-assisted proof (CAP) of the conjecture for four masses belonging to a closed domain in the mass space. The proof employs the Krawczyk operator and the implicit function theorem. Notably, we demonstrate that the implicit function theorem can be combined with interval analysis, enabling us to estimate the size of the region where the implicit function exists and extend our findings from one mass point to its surrounding neighborhood. Such methods may be applied to general nonlinear equations.
报告人简介：个人简介：谢之福博士现任美国南密西西比大学Wright W. and Annie Rea Cross基金会的数学和本科研究讲座教授，主要从事古典天体力学、微分方程及其在反应扩散方程和传染病模型等领域的应用研究。在2006年获得美国Brigham Young University数学博士学位。他于2007年开始在维吉尼亚州立大学任教，并在2015年晋升为教授。谢之福博士在研究、教学和服务等方面均表现突出，于2012年成为维吉尼亚州高等教育理事会（SCHEV）杰出教师奖的最终候选人之一。自2016年起，他加入了南密西西比大学担任Cross基金会的讲座教授。
