Mathematics professor discusses Differential Geometry with community

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On Thursday, September 28, the Union College Department of Mathematics Student Seminar welcomed Radcliffe Institute Fellow and John Wesley Young Research Instructor Professor Professor Megan M. Kerr for her talk: “What Can Symmetries Do for You? Shapes of Spaces.” Professor Kerr received her undergraduate degree at Wellesley College and her doctorate in mathematics at the University of Pennsylvania, studying Homogeneous Einstein Metrics. Professor Kerr currently teaches at Wellesley College, and has previously taught at the University of Arizona and Brown University. Her research is in Riemannian geometry, especially Lie groups and homogeneous spaces. She focuses on invariant metrics, such as Einstein metrics, positive curvature metrics and soliton metrics. Her talk addressed Differential Geometry, the study of shapes, and explored a special class of spaces with a high degree of symmetry. Specifically, when you manipulate the shape of a certain manifold and control the variations so that most of the symmetries remain. Professor Kerr began her talk by introducing groups of symmetries, specifically Lie groups. She first defined a Lie group as “a group and a topological space and compatibility condition.” She presented five examples of a Lie group and converted these to Lie algebra to better visualize the geometric shape. She stated, “The amazing thing about Lie groups and Lie algebra is how much of the geometry of the group is encoded in the corresponding Lie algebra.” She concluded, after displaying her work of Lie algebra on the board for the audience, that as you move and manipulate a sphere in various directions, a horizontal plane in the center maintains equal distance from a consistent point on the sphere. She stated, “Groups and geometry inform each other.” She used groups in a way that she called “cheating” because her work provided a unique approach on geometric shapes and allowed her to gather insight into geometry. Her work is significant because it helps provide a foundation on how to view geometric shapes and their movement and can be applied to a broad selection of issues in physics and medicine. The next event in the Student Seminar Talks has not been scheduled, but the Department of Mathematics plans to continue the Seminar later this term.

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