UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Friday (04/30/2004) at 2:00pm in 304 Pickard Hall

Speaker: Ruth Gornet, Department of Mathematics, University of Texas at Arlington

"Inverse Spectral problems and the Length spectrum"

Abstract: Can you hear the shape of a drum?'' is a problem popularized by Kac in the 1960s. We discuss the mathematical formulation of this problem, its generalization to higher dimensions, and historical and recent progress, including open problems. We then discuss why, analytically, it is natural to conjecture that if two objects sound the same, ie, have the same spectrum of the Laplace-Beltrami operator, they should have the same length spectrum, ie, periodic trajectories or lengths of closed geodesics. We close with recent work of the speaker toward better understanding the relationship(s) between the Laplace spectrum and the length spectrum.