Fall 2013

Laplacian Eigenvalues, Metric Uniformization, and Incidence Geometry

Thursday, Dec. 5, 2013 3:00 pm3:45 pm PST

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I will talk about using flows to "uniformize" graphs, endowing them with a geometry that emphasizes certain aspects of their global structure. In analogy with conformal uniformization on surfaces, one can use these geometries to study the spectrum of the graph Laplacian. In particular, we resolve some conjectures of Spielman and Teng on low-dimensional graphs, and offer a different resolution of a conjecture of S. T. Yau about the spectrum of surfaces (previously solved by Korevaar in 1993).