Bienvenue
sur la page d’accueil de Thierry Vallée
Emails: vallee@pps.univ-paris-diderot.fr
vallee_th@yahoo.fr
Phone: + 33 (0)9 81 28 55 98
My third level education is threefold. I studied Philosophy, Mathematics
and Computer Science at the University Lyon III, Paris I and Paris VII, and at
the I.B.I.A (Institute of Applied Informatics, Paris). I also taught for three
years in Mathematics, Statistics and Computer Science at the University
Clermont 1 (France) and at Georgia Southern University (Georgia, U.S.). I
recently worked as a consultant for a continuing education centre. I developed
and designed courses in Mathematics, Statistics, Computing and Methodology.
.
After
a Ph.D. thesis in Mathematical Logic and Foundations of Computer Science at
the PPS laboratory in the
Mathematics Department of the University Paris VII (2001), I worked during 9
months as a post-doc for the department of Mathematics and Computer Science of
the University of Udine. My research was about a theory of classes due to Ennio Di Giorgi. Then, I joined
the Centre for Efficiency Oriented Langage directed by Michel Schellekens
from May 2003 to April 2007. The centre was originally created to develop a new
programming language “average complexity friendly” named MOQA. For the last
five years my research focused on Graph Theory; Hamiltonicity,
Cartesian products of hypergraphs, hyperflows and links between groups and graphs are the main
themes of this research.
My scientific interests cover a broad spectrum:
- Graph Theory and its applications (see Current research in Graph Theory)
-
Foundation of mathematics, including lambda-calculus theories and their models
- Semantics of programming languages
- Logic
- Time Analysis of algorithms
The three last subjects above were
intimately linked in the MOQA project developed in CEOL. MOQA is a programming language
(formerly named ACETT) which was especially designed by Michel Schellekens to facilitate the average time analysis of its
programs. MOQA is based on a
special data structure and an associated suite of operations. This special data
structure consists of a poset endowed with a strictly
increasing bijection between the poset
and a totally ordered set of labels. MOQA basic operations are then defined on
this twofold data structure, and thus are in particular poset
operations. I worked on
a model of these basic operations. This model was aimed to allow a better
understanding of their fundamental property, named "Random
Preservation". It gave rise to the definition of generalizations of MOQA
operations. I also developed different theoretical results about Random
Preservation and random preserving operations. As a future direction of
research, it could be interesting to explore the different existing logic and
typing techniques used to control the worst case complexity of programs, and
try to apply them to the average time analysis.
In parallel to my work on average
complexity, I developed collaboration on Graph Theory and its applications with
the Pr. Alain Bretto from the University of Caen
(France). We studied links between graphs, topologies and groups, and in
particular the notion of G-graphs. G-graphs are graphs induced from groups
introduced by Pr. Alain Bretto. They are strongly linked to Cayley
graphs, are more general, and have applications in network design and
cryptography. We developed also some new conditions to decide hamiltonicity of graphs based on clique decomposition. We
are currently working on closure concepts linked with Hamiltonicity
as well as on Cartesian products of hypergraphs and hyperflows.
Title: "Map
Theory" et Antifondation,
defended on 21 December 2001 and published as ENTCS Vol.79
My thesis was about a foundational theory based on
type-free lambda-calculus due to Klaus Grue and
called Map Theory. The original version of MT is a "well-founded"
one. It includes an induction scheme allowing to define
functions, and an induction principle for reasoning about these functions. It
was proved by Grue to be at least as powerful as ZFC+Well-Foundation.
Motivated by the development of coinductive methods
of definition and reasoning in computer science, I designed an "antifounded" version MTA of MT which I proved to be at
least as powerfull as ZFC+AFA, where AFA is the Aczel-Honsell-Forti's antifoundation
axiom. We proved the relative consistency of this new version in the framework
of the kappa-continuous semantics of lambda-calculus, which is a generalization
of Scott's (omega-)continuous semantics to any regular
cardinal kappa.
I worked on a non-well-founded theory of classes due
to De Giorgi and its embedding in MTA. In particular, I attempted
to build a model of the theory plus a problematic axiom inside a model of MTA.
The question of the existence of such a model is still open.