This $246,525 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research at the University of California, Irvine (UC Irvine) across three main focus areas:
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Advancing spectral theory, several complex variables, and the geometry of Laplacian eigenfunctions, which are crucial for understanding how geometric structure influences spectral properties in mathematics and mathematical physics.
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Investigating strong inverse spectral results for generic polygons and extending prior work on nearly circular ellipses to generalize such results to generic ellipses and domains with constant width.
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Collaborating with Hang Xu to study asymptotic properties of Bergman kernels, including establishing new off-diagonal asymptotics and improving bounds for Bergman kernels on manifolds with real analytic boundaries.
The research conducted under this award will contribute to education and diversity through graduate student and postdoctoral researcher supervision, as well as outreach activities like math competitions and summer research programs for underrepresented students. The project period is from July 1, 2024 to June 30, 2027.
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