Deterministic and Stochastic Methods in the Study of Certain Evolution Models

Research Contract within the Excellence Research Programme of ANCS
Nr. 2-CEx06-11-18/2006

(romanian version)

International Cooperations:
  1. the five years AMAMEF programme (Advanced Mathematical Methods for Finances) organized by European Science Foundation, where the IMAR has co-authored the proposal;
  2. the European Network GDR - Mathematique et Physique Quantique organized by theCNRS (France);
  3. the international cooperation project: "Aspects mathématiques: du transport fermionique dans les systèmes mésoscopiques et les nanosystèmes et dans les cristaux ioniques; du scattering par des surfaces périodiques" between the IMAR and the CPT-Marsilia, (within the inter-academic agreement between the Romanian Academy and the CNRS -France);
  4. cooperation with the SPECT project of the European Science Foundation in organizing the 10-th edition of the International Conference Quantum Mathematics.
  1. Refining the variational method of solving determinist equations.
  2. Advanced methods in the study of stochastic differential equation; applications in Financial Mathematics and System Analysis.
  3. The study of Schroedinger operators by operatorial and potential methods.
  4. The study of certain algebras of pseudo-differential operators which appear in the mathematical description of the evolution of some quantum systems.
  5. Building up methods of interest in the study of certain physical systems and obtaining results concerning these methods: the study of the backscattering transform, equations of motions generated by linear Hamiltonians associated with the the Jacobi group; constructing models of super-symmetric Lagrangians.