Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, March 05, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Anna Gundert

A Cheeger Inequality in Dimension 2

The combinatorial expansion properties of a graph are closely related to the spectra of its Laplacian. We will discuss the discrete Cheeger inequality which expresses this relationship and will in particular see how we can prove that a large spectral gap implies edge expansion. We will then consider how this can be generalized to 2-dimensional simplicial complexes.
A generalization of the graph Laplacian was introduced by Eckmann in the 40s. Some might remember a result I presented last year: A large spectral gap for Eckmann's Laplacian doesn't imply a higher dimensional analogue of edge expansion that was recently introduced by Gromov, Linial and Meshulam, Newman and Rabinovich.
Now, I will present a positive result by Parzancheski, Rosenthal and Tessler that uses a different, more combinatorial analogue of edge expansion and relates this to the spectral gap of Eckmann's Laplacian.

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