Boundary Integral Methods, Eigenvalues and Computational Spectral Geometry

Explore boundary integral methods for computing eigenpairs of constant elliptic operators in this distinguished lecture on computational spectral geometry. Learn how to transform volumetric eigenproblems into boundary-based problems, achieving high accuracy and efficiency for complex domains. Discover techniques applicable to both smooth boundary domains and polygonal domains, with the speaker demonstrating how this approach reduces computational complexity by working on boundaries rather than entire volumes. Examine applications in spectral geometry and understand how these methods can address challenging eigenvalue problems that are difficult to solve using traditional approaches. The presentation focuses on planar problems while highlighting how the methodology extends naturally to three-dimensional spaces, making it valuable for researchers working with partial differential equations and computational mathematics.