Abstract
The problem of sampling convex bodies (and logconcave densities) in high dimension has led to the development of a number of useful techniques, both algorithmic and analytic, such as isoperimetric inequalities and tools to analyze the convergence of Markov chains. In this talk, we will survey the state-of-the-art of the complexity of sampling, both in theory and in practice, paying special attention to the case of uniformly sampling polytopes.