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This lecture features Matthew Faust (Michigan State University), Stephen Shipman (Louisiana State University), and Frank Sottile (Texas A&M University) discussing Spectral Theory as part of the Fields Institute's commutative algebra applications series scheduled for Tuesday, May 27, 2025. Explore fundamental concepts and recent developments in spectral theory, examining its applications in mathematical physics, differential equations, and algebraic systems. The 44-minute presentation connects theoretical frameworks with practical applications in the field of commutative algebra.