PRESENTATION 
The Institute of Mathematics of Luminy was created on January 1, 1996 starting from the old Laboratory of Discrete Mathematics (19921995). The IML is a UPR (Unit of Search) of the CNRS which scientifically depends on Department SPM (Physical sciences and Mathematics) and administratively on the Regional Delegation Provence accomodating a good number of teacherresearchers of the Faculty of Science of Luminy (which belongs to the University of the Mediterranean). The Institute of Mathematics of Luminy is located on the campus of Luminy . 
The topics approached by our 5 teams of search are as follows:
Into Arithmetic and Information theory , it is necessary to note the use of increasingly sophisticated methods of algebraic and arithmetic geometry (elliptic and modular curves, ladic cohomology). The use of processes of construction of abelian varieties leads to the development of cryptosystems. In addition, the theory of the polyhedrons of Klein is connected to that of the toric varieties, which joined the concerns of the singularists of the laboratory. Substantial improvements of central results into arithmetic (theorem of BrauerSiegel, limits of Weil) were obtained. Dynamics, Arithmetic and Combinatorics , the principal topic is complexity: complexity of continuations (combinatorics, arithmetic, concepts of random continuation), dynamic complexity and entropy, without forgetting invariant measurements and time of return. These subjects create bridges with physics (pavings, chaos) and data processing (languages, combinatorics), which justifies the interactions, in particular with the Center of Theoretical Physics (CPT). Two topics applied, the study of the quasirandom continuations for the integration of the type AssemblesCarlo and that of the genetic sequences. The transverse team "Mathematics of the Genome" (Imlcptlatp), lodged with the IML, uses various mathematical methods to answer some of the questions put by the biologists. In NonCommutative Geometry , the principal subjects studied in noncommutative geometry are the algebras of operators and the representations of groups, like their links with topology, the geometry and theoretical physics. The current topics of search include/understand the opératorielle Ktheory, the cyclic cohomology, the noncommutative harmonic analysis, the underfactors and several mathematical aspects of the quantum theory of the fields and statistical mechanics, such as the theory in conformity of the fields and the quantum groups. There is a weekly seminar organized jointly with the team corresponding of the Center of Theoretical Physics like with close mathematicians of disciplines to ChâteauGombert. Logic of the Programming , France plays an essential role, in Paris around JL Krivine and Marseilles around JY Girard. The federator topics are lambdacalculation and linear logic. The team works in particular on the mathematical interpretation of the evidence: networks (proof = graph), dénotationnelle semantics (proof = function), and ludic (proof = strategy). Its work arouses the interest of the dataprocessing community in the fields of the functional programming, the logical programming, the automatic demonstration and the models of parallelism. Lastly, the Singularities are approached since the points of view of the singularities of space (homology of intersection, characteristic classes) and of the singularities of applications (complex singularities of surfaces, homology bivariante), this last topic in interaction with the Analysis laboratory Topology Probabilities (LATP). 
For more information, consult the Report of the Activities 19992000 of the IML : Report 19992000.
Last update: October 12, 2001, EL.
