Dirichlet forms are a generalization of the Laplacian operator which can be used to study harmonic functions on measure spaces without mentioning partial derivatives. This allows mathematicians to study the Laplace and heat equations on non-manifold spaces, such as fractals, without needing a gradient operator. The Dirichlet form can even weakly define a "Laplacian" in this manner.
Stanford University
Autumn 2022
The course addresses both classic and recent developments in counting and sampling. It covers counting complexity, exact counting via determinants, sampling via Markov chains, and high-dimensional expanders.
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