# Kolloquium: Michael Baake (Universität Bielefeld): "The Markov embedding problem revisited (from an algebraic perspective)"

The Markov embedding problem revisited (from an algebraic perspective) – Vortragender: Michael Baake, Universität Bielefeld – Einladender: C. Richard

It is an old question whether a given Markov matrix can occur in a Markov semigroup, which became quite famous through a foundational paper by Kingman from 1962. Apart from some general characterisations (which are rarely useful in practice), a complete answer was given for 3×3 matrices by the mid 1990s, both for the homogeneous and the inhomogeneous case, after which the interest in it faded due to lack of applications.

This changed with the rise of bioinformatics and the study of stochastic processes on the basis of the nucleotide alphabet (A, G,C,T), which at least requires an answer for 4×4 matrices, which was given only recently. In this talk, the problem will be reviewed, and some of the recent progress discussed, with focus on practically useful results and on the underlying algebraic structure.