This $129,987 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research by The Johns Hopkins University on how the geometric properties of manifolds impact the behavior of eigenfunctions, which are the fundamental modes of vibration. The principal investigator will study "global harmonic analysis" techniques to develop improved estimates for the size and concentration of eigenfunctions, specifically examining how the geometry and global dynamics of the geodesic flow affect these estimates. The research aims to advance understanding of high-frequency solutions and spectral asymptotics for wave, Schrödinger, and metric Laplacian equations. This award provides research training opportunities for graduate students and aligns with NSF's goals of supporting pioneering scientific discoveries and developing the STEM workforce.
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