# Goal of the session

Polynomial systems are fundamental mathematical objects and emanate naturally in almost the whole spectrum of science. They arise in computational geometry, optimization, tensor decomposition, game theory, coding theory, cryptology, CAD, signal processing, robotics, biology; just to mention few of the disciplines.

Groebner bases, on the other hand, are one of the main tools for solving systems of polynomial equations. Moreover, they are the building blocks for a wide range of higher-level computer algebra algorithms.

The special session focuses on algorithms, efficient implementations for solving polynomial systems and on novel applications that extend the limits of the state-of-the-art from a theoretical and/or practical point of view. Its purpose is to bring together different communities that are interested in polynomial system solving, to present cutting-edge results in the area and to identify future challenges.

We explicitly encourage submissions on computational aspects.

The proposed special session is a follow-up of the successful special session "Groebner bases and applications" organised in the context ACA 2014 in New York.

## Contributed Talks

Anissa Ali | An algebraic method to compute the mobility of closed-loop overconstrained mechanisms |

Jérémy Berthomieu | Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials:The Regular Case |

Jinsan Cheng | Solving polynomial system with linear univariate representation |

Christian Eder | Improved Parallel Gaussian Elimination for Gr\"obner Bases Computations in Finite Fields |

Nadia El Mrabet | Use of Groebner basis in order to perform a fault attack in pairing-based cryptography |

Ioannis Emiris | Sparse multihomogeneous systems, root counts and discriminants |

Jean-Charles Faugere | Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences |

Robert H. Lewis | Solving Polynomial Systems Using the Dixon-EDF Resultant with Emphasis on Image Analysis Problems |

Anders Jensen | Tropical homotopy continuation |

Sharwan Kumar Tiwari | Modular Techniques to Compute Grooebner Bases over Non-Commutative Algebras with PBW Bases |

Gennadi Malaschonok | About Triangular Matrix Decomposition in Domain |

Matthew Niemerg | Bounds on the Number of Real Solutions For a Family of Fewnomial Systems of Equations via Gale Duality |

Victor Pan | Real Polynomial Root-finding by Means of Matrix and Polynomial Iterations |

Sirani Perera | A Fast Euclid-type Algorithm for Quasiseparable Polynomials |

Ludovic Perret | Algebraic Attack against Wild McEliece & Incognito |

John Perry | Midway upon the journey |

Guenael Renault | Application of Computer Algebra in Number Theory Based Cryptology |

Ludo Tolhuizen | The HIMMO Scheme |

Elias Tsigaridas | Nearly optimal algorithms for real and complex root refinement |

Tristan Vaccon | Computation of Groebner bases and tropical Gröbner bases over $p$-adic fields |

Chun-Ming Yuan | Efficient Groebner bases computation for Z[x] lattice |

# Organizers

- Christian Eder (University of Kaiserslautern, Germany)

Contact: ederc@mathematik.uni-kl.de - Jean-Charles Faugère (UPMC, INRIA PolSys Team, Paris, France)

Contact: Jean-Charles.Faugere@inria.fr - Ludovic Perret (LIP6-UPMC/CNRS/Inria, Paris, France )

Contact: ludovic.perret@lip6.fr - Elias Tsigaridas (UPMC, INRIA PolSys Team, Paris, France)

Contact: Elias.Tsigaridas@inria.fr