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Tuesday, December 3, 2019

**Abstract:** We consider the Steklov eigenvalue problem on curvilinear polygons in the plane, with all interior angles measuring less than pi. In this setting, we formulate and prove precise spectral asymptotics, with error converging to zero as the spectral parameter increases. These asymptotics have a surprising dependence on arithmetic properties of the angles. Moreover, the problem turns out to have an interesting relationship to a scattering-type eigenvalue problem on the one-dimensional boundary of the polygon, viewed as a quantum graph.