Closed Geodesics in 2-Step Nilmanifolds (Mathematics)

研究活动将集中于两步幂零度量李群的测地线行为。研究给定李群几何的一个成功方法是检查其相关李代数的代数结构。特别强调的是奇异李群。奇异性是由在相关李代数的中心上定义的一组偏对称线性变换的奇异性决定的。Maura Mast博士打算将以前研究两步幂零非奇异李群的几何方法应用到奇异李群的研究中。她还打算将她关于两步零流形中封闭测地线长度的研究结果应用于光谱几何问题。互动活动包括：教授研究生水平的可微流形课程和微积分入门课程；积极参加东北大学和波士顿地区其他学校的研讨会；与东北大学合作，制定招聘和留住数学专业学生的方法；并为科学和数学领域的女性发起讨论和支持小组。

Research activities will focus on geodesic behavior in 2-step nilpotent metric Lie groups. One successful approach to studying the geometry of a given Lie group is to examine the algebraic structure of its associated Lie algebra. Particular emphasis will be given to Lie groups which are singular. Singularity is determined by the singularity of a set of skew-symmetric linear transformations defined on the center of the associated Lie algebra. Dr. Maura Mast intends to use apply previous methods used in the study of the geometry of 2-step nilpotent nonsingular Lie groups to the study of singular Lie groups. She also intends to apply her results on lengths of closed geodesics in 2-step nilmanifolds to problems in spectral geometry. Interactive activities include: teaching a graduate level Differentiable Manifolds course and a beginning Calculus course; participating actively in seminars at Northeastern University and other school in the Boston area; working with Northeastern University to develop methods to recruit and retain math majors; and initiating discussion and support groups for women in science and mathematics.