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Explore a seminar talk on spectral geometry that delves into the application of equivariant optimization of Laplace and Steklov eigenvalues on surfaces to construct embedded minimal surfaces in the 3-sphere and 3-ball. Learn about joint work by McGrath, Karpukhin, Kusner, and Stern, which builds upon Daniel Stern's previous presentation. Discover how Riemannian metrics maximizing normalized eigenvalues lead to branched minimal immersions by first eigenfunctions into spheres and balls. Examine the concept of Basic Reflection Surfaces (BRS) and their role in ensuring codimension-1 embeddings. Gain insights into the existence of orientable, embedded minimal surfaces with free boundary in the 3-ball, addressing a question posed by Fraser and Li. Engage with advanced mathematical concepts in this 58-minute presentation from the Spectral Geometry in the clouds seminar series.
