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Friday, February 28, 2020

**Abstract:** Recently there has been a growing interest in eigenvalues on forms. It is much more complicated than eigenvalues on functions but can detect finer geometry. It has applications in detecting length of axes of John ellipsoid of convex body, relating Monopole Floer homology to hyperbolic geometry, and commutator length in hyperbolic geometry. In this talk we will show some basic theory and definitions for eigenvalues on forms, and then provide some intuition for the geometry and applications.