SALSA   LIP6 Calcul Scientifique UMPC

ACA 2014 Special Session: Gröbner bases and applications

****** July 9 - 12, 2014 - Fordham University - New York, New York


  • Christian Eder (University of Kaiserslautern, Germany)
  • Jean-Charles Faugère (UPMC, INRIA PolSys Team, Paris, France)
  • Michael Stillman (Cornell University, Ithaca, NY, US )

Goal of the session

Gröbner bases are a fundamental tool in computer algebra with many applications in various areas. In 1965 Buchberger introduced a first algorithmic approach for their computation. For many high-level computer algebra algorithms Gröbner bases act as building blocks. Over the years many improvements and optimizations on the theory of Gröbner bases, but also advances in computer science and hardware, led to efficient implementations. Moreover, Göbner bases have various applications, for example, in the fields of robotics and cryptography that underline the importance of this field of computational algebra. The aim of this session is to gather researchers with an interest in the theory of Gröbner bases as well as those focussing on efficient implementations. We explicitly encourage submissions on computational aspects.


TALKS in the session (tentative schedule of the session)

(be careful that our session is on Thursday 10 afternoon and Sartuday 12 morning).

  • Gora Adj, Computing Discrete Logarithms using Joux's Algorithm - Abstract in pdf
  • Ambedkar Dukkipati, On Groebner bases over rings and residue class polynomial rings with torsion Abstract in pdf
  • Christian Eder A survey on signature-based Gröbner basis computationsAbstract in pdf
  • Jean-Charles Faugere, Sparse Groebner Bases: algorithms and complexity Abstract in pdf
  • Ludovic Perret, Algebraic Algorithms for Learning with Errors Problems (LWE) Abstract in pdf
  • John Perry, The skeletons you find when you Order your Ideal’s Closet Abstract in pdf
  • Matthew Tamayo Algebraic cryptosystems and vulnerability to Groebner basis attacks Abstract in pdf
  • Sun, Lin, Wang, On Implementing Signature-based Grobner Basis Algorithms Using Linear Algebraic Routines from M4RI Abstract in pdf


Session topics will include (but are not limited to) the following:

  • All aspects of new advances in computing Gröbner bases, for example
    . F5-like resp. signature-based algorithms,
    . specialized linear algebra,
    . advances in parallel implementations,
    . exploitation of algebraic structures,
    . computations and utilizations of syzygies.
  • Recent results in complexity theory on (specialized) Gröbner basis computations.
  • Actual applications that demonstrate the efficiency of Gröbner bases for specific problem solving.