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Wednesday, August 29, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, August 29, 2012
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Submitted by laugesen.
Richard Laugesen   [email] (UIUC Math)
Eigenvalues of the Laplacian
Abstract: The fundamental processes of classical physics are diffusion and wave motion. Quantum mechanics too is a kind of wave phenomenon. Mathematically, these processes can all be decomposed in terms of eigenfunctions (states) and eigenvalues (frequencies) of the Laplacian (the sum of pure second partial derivatives). What do we know about those eigenvalues? What would we like to know? I will concentrate on isoperimetric problems that stretch back to Queen Dido in antiquity and Lord Rayleigh in the 19th century, and continue into the future.