Bienvenue sur la page d’accueil de Thierry Vallée
Emails: vallee@pps.jussieu.fr
vallee_th@yahoo.fr
Phone: + 33 (0)1 77 48 22 81
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, I worked
during 9 months as a postdoc for the
department of Mathematics and Computer
Science of the University of Udine. Then, I joined the Centre for Efficiency Oriented Langage directed by Michel Schellekens
from May 2003 to April 2007. Finally I worked for one year as an Assistant
Professor in Mathematics and Statistics at Georgia Southern University
(Georgia, US).
During my PhD, I had got a two years lectureship position as an ATER in
Mathematics and Computer Science. My lectures took place in the GEA department
of the IUT of the University Clermont1
, and my research at the LLAIC,
a laboratory of the same university.
My scientific interests cover a broad spectrum:
- Foundation of mathematics, including lambda-calculus theories and their
models
- Graph Theory and its applications
- Semantics of programming languages
- Logic
- Time Analysis of algorithms
The three last subjects are 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 a
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.
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.