The Spectrum of Sparse Random Complex
Session Number
O04
Advisor(s)
Dominic Dotterrer, University of Chicago
Location
B-116
Start Date
28-4-2016 9:15 AM
End Date
28-4-2016 9:40 AM
Abstract
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, randomized algorithms, and graph theory. It contains information that describes certain properties of the graph. One important set of information is its set of eigenvalues (also known as its spectrum). For example, one can determine the relative connectivity of a graph with this. Furthermore, one can determine global geometric properties through the spectrum. The graph Laplacian can be extended to simplicial complexes (higher dimension versions of graphs). The importance of the graph Laplacian therefore leads us to study the Laplacian for simplicial complexes. Through this operator, one can quantitatively measure the vanishing of cohomology – in other words a measure of higher dimensional connectivity. This investigation will present the ideas that have been researched
The Spectrum of Sparse Random Complex
B-116
The combinatorial Laplacian is an operator that has numerous applications in physics, finance, randomized algorithms, and graph theory. It contains information that describes certain properties of the graph. One important set of information is its set of eigenvalues (also known as its spectrum). For example, one can determine the relative connectivity of a graph with this. Furthermore, one can determine global geometric properties through the spectrum. The graph Laplacian can be extended to simplicial complexes (higher dimension versions of graphs). The importance of the graph Laplacian therefore leads us to study the Laplacian for simplicial complexes. Through this operator, one can quantitatively measure the vanishing of cohomology – in other words a measure of higher dimensional connectivity. This investigation will present the ideas that have been researched