Graphs, Vectors, and Matrices
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 45.0-61, 2017.
This survey accompanies the Josiah Williard Gibbs Lecture that I gave at the 2016 Joint Mathematics Meetings. It provides an introduction to three topics: algebraic and spectral graph theory, the sparsification of graphs, and the recent resolution of the Kadison-Singer Problem. The first and third are connected by the second.
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