Acknowledgments Many thanks to the Dagstuhl office and its helpful and patient staff; huge thanks to the organizers of the previous seminars in the series for setting us up for success; and thanks to all  ...  the participants, who worked hard and were amiable company all week.  ...  The Shub and Smale's "tau-conjecture" states that the number of integer roots of a univariate polynomial should be polynomially bounded in the size of the smallest straight-line program computing it.  ...