Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research.

C. Andradas: Characterization and description of basic semialgebraic sets

D. Bailey and V. Powers: Constructive approaches to representation theorems in finitely generated real algebras

I. Bonnard: Combinatorial characterizations of algebraic sets

P. Burgisser: Lower bounds and real algebraic geometry

B. Chevallier: The Viro method applied with quadratic transforms

A. Gabrielov and T. Zell: On the number of connected components of the relative closure of a semi-Pfaffian family

C. McCrory: How to show a set is not algebraic

P. A. Parrilo and B. Sturmfels: Minimizing polynomial functions

B. Reznick: Patterns of dependence among powers of polynomials

F. Rouillier: Efficient algorithms based on critical points method

F. Sottile: Enumerative real algebraic geometry

I. Streinu: Combinatorial roadmaps in configuration spaces of simple planar polygons

T. Theobald: Visibility computations: From discrete algorithms to real algebraic geometry

C. Andradas: Characterization and description of basic semialgebraic sets

D. Bailey and V. Powers: Constructive approaches to representation theorems in finitely generated real algebras

I. Bonnard: Combinatorial characterizations of algebraic sets

P. Burgisser: Lower bounds and real algebraic geometry

B. Chevallier: The Viro method applied with quadratic transforms

A. Gabrielov and T. Zell: On the number of connected components of the relative closure of a semi-Pfaffian family

C. McCrory: How to show a set is not algebraic

P. A. Parrilo and B. Sturmfels: Minimizing polynomial functions

B. Reznick: Patterns of dependence among powers of polynomials

F. Rouillier: Efficient algorithms based on critical points method

F. Sottile: Enumerative real algebraic geometry

I. Streinu: Combinatorial roadmaps in configuration spaces of simple planar polygons

T. Theobald: Visibility computations: From discrete algorithms to real algebraic geometry

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