Focal

FOrmalisation du Calcul ALgébrique / Formalisation of algebraic computation

This project is located at the interaction of algebraic topology and rewriting systems. The three main axes are the following:

Finding a unified context to apply in algebra the latest results of rewriting theory.
Developing algorithms for effective computations in algebra, including computing homological invariants for algebras and operads.
Implementing these algorithms in a way adapted at the same time for the context of rewriting and for the algebraic/operadic context.

The members of the project are hosted either by the laboratory PPS (Preuves, Programmes et Systemes) and the IMJ-PRJ at Universite Paris 7 or the algebraic topology team of the LAGA (Laboratoire Analyse, Geometrie et Applications) at Universite Paris 13.

Algebraic topology, rewriting systems, Groebner basis, homological invariants, higher dimensional rewriting, effective computation.

Pierre-Louis Curien (PPS)	http://www.pps.univ-paris-diderot.fr/~curien/
Yves Guiraud (PPS)	http://www.pps.univ-paris-diderot.fr/~guiraud/
Eric Hoffbeck (LAGA)	http://www.math.univ-paris13.fr/~hoffbeck/
Muriel Livernet (IMJ-PRG)	http://www.math.univ-paris13.fr/~livernet/
Philippe Malbos (ICJ and PPS)	http://math.univ-lyon1.fr/~malbos/
Francois Métayer (PPS)	http://www.pps.univ-paris-diderot.fr/~metayer/
Samuel Mimram (CEA and PPS)	http://www.pps.univ-paris-diderot.fr/~smimram/

Stephanie Ziegenhagen (from September 2014 to August 2015)

Cyrille Chenavier (advisors : Y. Guiraud and P. Malbos)

Cyrille Chenavier, Confluence algebras and acyclicity of the Koszul complex, preprint 2015.
Eric Hoffbeck and Christine Vespa, Leibniz homology of Lie algebras as functor homology, Journal of Pure and Applied Algebra 219 (2015), 3721-3742.
Yves Guiraud and Philippe Malbos, Polygraphs of finite derivation type,Math. Structures Comput. Sci. (to appear).
Yves Guiraud, Eric Hoffbeck and Philippe Malbos, Linear polygraphs and Koszulity of algebras, preprint.
Yves Guiraud, Eric Hoffbeck and Philippe Malbos, Confluence of linear rewriting and homology of algebras, International Workshop on Confluence 2014.
Muriel Livernet, B. Mesablishvili and R. Wisbauer, Generalised bialgebras and entwined monads and comonads, Journal of Pure and Applied Algebra 219 (2015) 3263-3278.