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This lecture covers the concept of Laplacian solvers, focusing on the approximate solution of Laplacian linear systems, optimal Laplacian solvers, and their applications in physics, engineering, and signal analysis. It delves into the theoretical and practical aspects of Laplacian solvers, including the scope of applications, error conversion, and improving solver theorems. The lecture also discusses models of computation in theoretical computer science, structured matrices, and the use of Laplacian solvers in various practical scenarios.