"The project Algebraic Algorithms and Applications (A3) is an interdisciplinary and multidisciplinary project, with strong international synergy.

It consists of four work packages
The first (Algebraic Algorithms) focuses on fundamental
problems of computational (real) algebraic geometry: effective zero
bounds, that is estimations for the minimum distance of the roots of a
polynomial system from zero, algorithms for solving polynomials and
polynomial systems, derivation of non-asymptotic bounds for basic
algorithms of real algebraic geometry and application of polynomial
system solving techniques in optimization.
We propose a novel approach that
exploits structure and symmetry, combinatorial properties of high
dimensional polytopes and tools from mathematical physics.

Despite the great potential of the modern tools from algebraic
algorithms, their use requires a combined effort to transfer this
technology to specific problems. In the second package (Stochastic Games)
we aim to derive optimal algorithms for computing
the values of stochastic games, using techniques from real algebraic
geometry, and to introduce a whole new arsenal of algebraic tools to
computational game theory.

The third work package (Non-linear Computational Geometry), we
focus on exact computations with implicitly defined plane and
space curves. These are challenging problems that commonly arise in
geometric modeling and computer aided design,
but they also have applications in polynomial optimization.

The final work package (Efficient Implementations) describes our plans
for complete, robust and efficient implementations of algebraic
algorithms."