Geometry/topology Seminar
Tuesday, October 2, 2018, 3:15pm, 119 Physics
Michael Lipnowski (McGill University, Mathematics)
The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds
Abstract:- We exhibit examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies hyperbolic geometry in an essential way; it combines an explicit upper bound for the first eigenvalue on coexact 1-forms \lambda_1^* on rational homology spheres which admit irreducible solutions together with a version of the Selberg trace formula relating the spectrum of the Laplacian on coexact 1-forms with the volume and complex length spectrum of a hyperbolic three-manifold. Using these relationships, we also provide precise certified numerical bounds on \lambda_1^* for several hyperbolic rational homology spheres. [video]
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