## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, August 27, 2013, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: May Szedlák

## On the Cheeger Inequality for Simplicial Complexes

The lower bound of the Cheeger inequality for a graph G estabilishes a connection between the spectral and expansion properties of the graph, namely \lambda(G) \leq h(G), where \lambda(G) is the second smallest eigenvalue of the Laplacian of G and h(G) the Cheeger constant. We consider a generalization of the above inequality for simplicial complexes. Parzanchevski, Rosenthal and Tessler showed, that for suitable generalizations of \lambda(G) and h(G) the inequality \lambda(X) \leq h(X) holds, if X is a k-dimensional simplicial complex with complete(k-1)-skeleton. I present that \lambda(X) \leq h(X) holds for arbitrary k-dimensional simplicial complexes.

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