Minimum Entropies of Braids

Every braid can be thought of as a homeomorphism of a punctured disc. Morally, the more complicated a braid is, the more dynamics is contained in the corresponding homeomorphism, which one can quantify using topological entropy. In particular, one can easily construct braids with arbitrarily large entropies. The situation is more interesting at the other end of the spectrum, where one can ask for the minimum entropy of braids (with a fixed number of strands). In this talk, we present joint work with Xiangzhuo Zeng in answering this question.