A mini-course on techniques for Rapidly Mixing Markov Chains in relation to Approximate Counting.
We will discuss approximate counting, and its relationship to uniform random generation. The focus will be on techniques for randomised approximation, in particular the Monte Carlo Markov Chain method. Two approaches to proving polynomial time convergence of Markov chains will be examined.

Prof. Dr. Martin E. Dyer is from the Computer Science Department of the University of Leeds. He has published over a 100 papers, the majority of them as publication in top-journals in the field or as contribution to proceedings of the most prestigious, highly selective, conferences in the field. Since over 20 years his main research topic is the study of rapidly mixing Markov Chains in relation to approximate counting. In 1991 he won the Fulkerson Prize of the Mathematical Programming Society for his work on computing the volume of convex bodies, essentially a counting problem. The approach is Markov Chain Monte Carlo simulation. The breakthrough was a polynomial bound on the convergence time of this Markov Chain. Since then he has become one of the authorities in this field of approximate counting and approximate uniform random generation. He developed several new techniques for establishing rapid mixing of Markov Chains. Some of these he will present in his two lectures.