European Network in Geometry,

Mathematical Physics and Applications

Enigma is a **
Marie Curie Research Training Network,
supported by the European Commission **under
the **Sixth Framework Programme (FP6)
**

Geometry traditionally plays a central role in the mathematical formalism of physics. The relationships between geometry and mathematical physics received a great impetus from the discovery of the integrability phenomenon. For example:

- the Korteweg- de Vries equation works not only in the theory of weakly dispersive nonlinear waves but also in two-dimensional quantum gravity as well as in the geometry of moduli spaces of algebraic curves.
- Matrix integrals, introduced in the statistics of nuclear energy levels, proved to be connected with quantum gravity, conformal field theory, solutions of soliton equations, moduli spaces, singularity theory, Gromow-Witten invariants.
- Random matrices and random permutation problems, including certain stochastic processes, have also appeared on the scene in relation with sorting problems in combinatorics, multivariate statistics and growth models.

The network comprises 10 partner nodes from 7 European Countries:

- SISSA (*) Scuola Internazionale Superiore di Studi Avanzati: Mathematical Physics Sector
- ETH Zurich Swiss Federal Institute of Technology Zurich: Department of Mathematics
- UOXF.BK The Chancellor, Masters and Scholars of the University of Oxford: Mathematical Institute
- UPMC Université Pierre et Marie Curie: Laboratoire de Physique Théorique et des Hautes Energies (CNRS-UMR 7589)
- UCL Université Catholique de Louvain: Mathematic Department
- KTH Kungliga Tekniska Hogskolan: KTH Mathematics
- Imperial College of Science, Technology and Medicine: Mathematics Department
- ENS École Normale Supérieure: Department de Mathématique Pure et Appliqueé (CNRS-UMR 8553)
- LU Loughborough University: Department of Mathematical Sciences
- TU Berlin Technische Universitat Berlin: Mathematisches Institut, Fakultaet 2

Active collaboration from other working groups and individuals is expected throughout the network's activity, which will last 48 months starting from