#
Algorithms in Real Algebraic Geometry: Recent Advances

## Richard Pollack (Courant Institute)

We shall describe the problems known as the "Existential Theory of the
Reals", the "General Decision problem for the reals" which are both
special cases of "Quantifier Elimination over real closed fields" and the
construction of "Roadmaps" for semi-algebraic sets. There is a long history
of algorithmic solutions to these problems going back sixty years to Tarski
followed by work of Collins, Schwartz-Sharir, Grigor'ev-Vorobjov, Heintz-
Roy-Solerno, Canny and Renegar among others. Then we shall indicate some of
the new ideas developed by Basu-Pollack-Roy that permit further improvements
in these algorithms.