Welcome to the home page of Thierry Vallée
Dr. Thierry Vallée
Assistant Professor
Dept. of Mathematical Sciences, P.O. Box 8093
Georgia Southern University
Statesboro, 30458 Georgia, US
Email: tvallee@georgiasouthern.edu
Phone: + (912) 486 77 41
Publications and
Pre-publications
Short academic CV
After a PhD 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. I am presently
Assistant Professor in Mathematics and Statistics at Georgia Southern
University.
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.
Scientifics interests
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 my current laboratory CEOL . MOQA is a
programming language (formerly called ACETT) which was especially
designed by Michel Schellekens to facilitate the average time analysis
of its programs. In
particular, I am working on a model of the basic operations of
MOQA. This model would allow a better understanding of the fundamental
property of MOQA's operations,
called "Random Bag Preservation". The general aim of this model
is then to help us to find new Random Structure Preservation
operations.
In a middle term run, I would like to explore the different logic
and typing techniques used to control the complexity of programs, and
try to apply them to the average time analysis.
In parallel to my work on average complexity, I am developing a
cooperation on Graph Theory and its applications with the Universities
of Caen and St. Etienne. We are studying links between graphs,
topologies
and groups. In particular, G-graphs, a certain kind of graphs
induced from groups introduced by Pr. Alain Bretto
and
strongly linked to Cayley graphs, have applications in network design
and cryptography.
PhD thesis:
Title: "Map Theory" et Antifondation, defended on 21
December 2001 and published as ENTCS Vol.79
My thesis was about a foundational theory of 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.
Postdoc in Udine
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.