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Title: Geometry of the smallest 1-form Laplacian eigenvalue on hyperbolic manifolds.
Abstract: I鈥檒l describe a relationship between the smallest 1-form Laplacian eigenvalue and surface complexity on hyperbolic manifolds. We'll then speculate on "surface theft", a prospect based on this relationship for proving good lower bounds on the smallest 1-form Laplacian eigenvalue for big congruence arithmetic hyperbolic 3-manifolds M. This is joint work with Mark Stern.