Closed Geodesics in 2-Step Nilmanifolds (Mathematics)

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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.