MATH Seminar

Title: Sum rules for eigenvalues of differential equations on surfaces and graphs
Seminar: Analysis and Differential Geometry
Speaker: Professor Evans Harrell of Georgia Institute of Technology
Contact: Vladimir Oliker, oliker@mathcs.emory.edu
Date: 2010-10-19 at 4:00PM
Venue: MSC W301
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Abstract: I will discuss ``sum rule'' identities that can be derived at the level of operator algebra, and their uses to prove sharp inequalities for eigenvalues of elliptic differential operators on manifolds and on metric graphs. Three uses of the sum rules are to find connections between Laplace spectra and curvature on "quantum waveguides," to find connections between Schr\"odinger spectra and topology on "quantum graphs," and to yield short, efficient derivation of sharp semiclassical estimates of Lieb-Thirring type in the same situations. Parts of this work are joint with Demirel, Hermi, and Stubbe.