Uli Walther Department of Mathematics, Purdue University, West Lafayette, Indiana, USA "Computational Algebraic Geometry and Switching Surfaces in Optimal Control" Some problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. In this note, we apply Gr"obner basis techniques and some facts from the theory of real systems to find effective solutions to the classical problem of time-optimal control.