A fundamental tool used in sampling, counting, and inference problems is the Markov Chain Monte Carlo method, which uses random walks to solve computational problems. The main parameter defining the efficiency of this method is how quickly the random walk mixes (converges to the stationary distribution). Prof. Anari from Stanford University gave a series of lectures on using log concave polynomials in analysis of random walks to sample and count bases of a matroid. The results have resolved multiple conjectures in combinatorics, probability theory and algorithms.
