# nLab Yves Guiraud

Yves Guiraud is a French mathematician and theoretical computer scientist. He is Chargé de recherche INRIA attached to INRIA Rocquencourt, but based in Irif PPS, at Paris 7. His main research is in rewriting systems, especially in higher dimensions.

His webpage is here.

The list of his preprints on the Arxiv is here

His thesis (2004) was

#### Thesis abstract

This thesis studies the computational properties of operad presentations, or Penrose diagrams rewrite systems, together with their links with classical types of rewrite systems. With new criteria for termination and confluence, the convergence of the presentation $L(\mathbb{Z}_2)$ of $\mathbb{Z}/2\mathbb{Z}$-vector spaces, a commutative equational theory, is proved. Operad presentations are shown to be generalizations of both word rewrite systems and Petri nets; furthermore, they provide explicit resource management calculi for left-linear term rewrite systems. This work is concluded by the description of obstructions for proving the same result for the lambda-calculus. Two appendices present the links between operads and other structures from universal algebra, together with a calculus of explicit substitutions.

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