Nevanlinna Prize Talk:
I will explain some of the most interesting applications of solving linear equations
in Laplacian matrices as well as some of the most interesting ideas that have been
used in algorithms that solve these equations. The main applications will come from
machine learning and optimization. The algorithmic ideas I discuss will
include local clustering, sparsification, low-stretch spanning trees, and an under-appreciated
technique of Lovasz and Simonovits for bounding the convergence rate of Markov chains.