Algorithmic problem of recognition of quasipositive braids and its relation to plane algebraic curves

A braid is called quasipositive if it is a product of conjugates of the standard generators of the braid group. Quasipositive braids naturally appear in the study of plane algebraic curves. The algorithmic problem to decide whether a given braid is quasipositive is still open. Some partial results in this direction will be presented in the talk.