Aller à : contenu haut bas recherche
EN     FR
Vous êtes ici:   UNIL > HEC Inst. > HEC App. > RECHERCHE

Jacques Duparc


Professeur ordinaire
Département des opérations

Anthropole, bureau 3086
Tél 021.692.35.88

Adresse postale
Université de Lausanne
Quartier UNIL-Chamberonne
Bâtiment Anthropole
1015 Lausanne

Page personnelle :


master Computational Complexity I
Formations concernées
Maîtrise universitaire ès Sciences en management, Orientation marketing
Maîtrise universitaire ès Sciences en management, Orientation comportement, économie et évolution
Maîtrise universitaire ès Sciences en management, Orientation business analytics
Maîtrise universitaire ès Sciences en management, Orientation stratégie, organisation et leadership
bachelor Introduction à la logique
Formations concernées
Baccalauréat universitaire ès Sciences en management
Baccalauréat universitaire en sciences économiques


Axes de recherche

Borel mappings via games and representation theorems
We characterize some classes of Borel functions over the Baire space as strategies in suitable games. This is a way towards both obtaining representation theorems and elaborating a fine classifications of Borel functions. Representation theorems come as a representation of some classes of functions very different from their definitions. For instance, a cornerstone for this type of result is the Baire Grand Theorem which states that the following are equivalent for any function f on a Polish space:

- f is the pointwise limit of countably many continuous functions;
- on every non-empty closed subset f admits a point of continuity.

Continuous Reductions on Quasi-Polish spaces
Quasi-Polish spaces is a novel unifying theory due to Matthew de Brecht. It brings together topological structures that were previously unrelated. It connects closely topology in mathematical analysis -- which is usually Hausdorff (T_2) -- to topology in computer science -- which is rather Kolmogorov} (T_0) -- by offering the Polish spaces as well as the omega-algebraic or omega-continuous domains a common roof. Quasi-Polish spaces are derived from Polish spaces -- which are separable completely metrizable topological spaces -- by simply relaxing the symmetry condition in the definition of a metric.

We propose to design and make use of game theoretical tools to study the reductions between these sets and explore the underlying ordering as well as
the natural hierarchies that would arise. We intend to do this in a similar manner as the way we studied the Wadge hierarchy of Borel subsets of the Cantor space.

Quotients of Projective Fraïssé Limits
The idea of studying infinite structures via approximation by finite structures is a well rooted concept in mathematics. In particular, the Fraïssé limit is an extensively studied tool in many areas of mathematics.
In 2006 T. Irwin and S. Solecki introduced the projective Fraïssé limit of topological structures. Many applications have since been found in continua theory and descriptive dynamics.
We propose to isolate and study the class of all compact metric spaces that are obtainable as a quotient of a projective Fraïssé limit by the interpretation of a binary relation symbol from the language. Our hope is to describe a natural way of obtaining such spaces.

The Wadge Hierarchy
Over a century ago, the modern theory of integration, based on measure theory induced a fundamental interest in the study of well-behaved subsets of the real line or the real plane. Topology, which developed about the same time yielded the mathematical framework for such a study. For instance, the σ-algebra generated by the open subsets proved to be central in measure theory, for the sets it defines bear all desired nice properties.

The most refined classification of these sets is the so-called Wadge hierarchy whose study involves methods from (set theoretical) game theory

Topological Complexity, Games, Logic and Automata
We try to unravel the fine topological structure of omega-regular tree languages which are the infinitary languages of trees recognized by automata. In other words, we exhibit the Wadge hierarchy of non deterministic omega-tree automata.


this section is under maintenance

please refer to the author in unisciences



Cours donnés à l'EPFL

Logique mathématique
Fondement des mathématiques (théorie des ensembles) et fondement de l'informatique (informatique théorique).


Doctorat de mathématiques
Université Paris VII-Denis Diderot, (1995)


  • informatique théorique
  • logique mathématique
  • théorie descriptive des ensembles


Internef - CH-1015 Lausanne - Suisse  -   Tél. +41 21 692 33 00  -   Fax +41 21 692 33 05
Swiss University