Mathematics
Department

The Laurent Schwartz Center for Mathematics

The Mathematics Centre was founded by Laurent Schwartz in 1965 and was one of the first École Polytechnique laboratories. It took the name of Laurent Schwartz Mathematics Centre (CMLS) on 1st January 2004 as a tribute to its founder.
The Centre aims to carry out research at the highest level and develop the teaching of mathematics at École Polytechnique and at the University. It seeks to attract the most gifted young people in the discipline towards this domain and to pass on to as many people as possible the idea that mathematics is also - but not only - an essential instrument for understanding the world.
The three teams - algebra, analysis and geometry - organise a joint colloquium with the applied mathematicians and I.T. students.
The team organises the Quantum Group Seminar and working groups in Algebraic Geometry, which are intended for doctoral students or experienced researchers. The analysis team's research covers the various aspects of the partial derivative equations theory.
In fact, there is a great deal of variety to be found within this theme.
Firstly, the methods and tools used require significant developments related to harmonic analysis, symplectic geometry, complex analysis, functional analysis and topological methods for an analysis of the critical points of functionals.
Secondly, although certain aspects of our work focus on general classes of PDE, others study equations or systems modelling a wide variety of phenomena relating to physics or mechanics. The team also organises the Partial Derivative Equations seminar and a joint working group with CMAP.
The main areas of research covered by the geometry team may be grouped under following headings: negative curve varieties geometry, Ergodic geometry and dynamic systems, symplectic topology, index theorems and Diophantian geometry of convex polytopes. The teams organises the A. Besse seminar on Riemannian and complex geometry, the Ergodic geometry seminar, the symplectic topology seminar and a number of working groups.
CMLS plays an active role in training through research: X-UPS days organised for teachers of preparatory classes for scientific grandes écoles, Master's program tuition and optional courses for École Polytechnique students. The student and doctoral seminars take place once a week and an autumn seminar is organised for 3rd year Polytechnique students to give them an opportunity to see mathematics interacting with the other sciences.