报告题目：短期课程: Moments of Weighted Systems and Applications

报 告 人：Eduardo S. G. Leandro 教授（Federal University of Pernambuco, 巴西佩尔南布科联邦大学）

报告时间：2025年9月28日（星期日）9:00—10:30; 2025年9月30日（星期二）9:00—10:30.

报告地点：数学科学学院114（小报告厅）      

校内联系人：赵磊 教授         联系方式：84708351-8625

报告摘要：The goal of this minicourse is to present the basic theory of moments of systems of weighted points with an emphasis on the application to general equilibrium problems from Classical Mechanics and possibly other areas.

第一讲: We provide the basic results on moments of weighted systems in affine Euclidean spaces which are necessary to formulate equilibrium equations in terms of mutual distances and/or volume barycentric coordinates. If time allows, we will also discuss constraints for mutual distances of configurations imposed by dimension or cocircularity.

第二讲: We discuss applications to central configurations of the n-Body Problem. We will show how to formulate well known central configuration equations as well as deduce new ones, all of which are either independent of the configuration's dimension or hold for configurations of any given dimension.