The Group of Mathematical Physics of the University of Lisbon is working in a plain new and comfortable research centre, located 15 minutes away from the airport and with easy transportation to the centre of Lisbon. All scientific facilities are available in this institute, as well as housing for short term visitors.
Our scientific team is composed by A.B.Cruzeiro, J.Rezende, J.C. Zambrini, associated PhD and Postdoc collaborators. The main contribution of the group, inside the European project, is twofold. On one side, we develop the analysis and geometry of the path space in the perspective of Malliavin Calculus (ref.1). In this field there is an interplay between infinite dimensional geometry and stochastic analysis as well as a possibility of applications in theoretical physics: a postdoc in this area would divide time with France (Prof.Malliavin) and Germany (Profs. Albeverio and Roeckner).
On the other hand, we use techniques of stochastic analysis to develop a probabilistic counterpart of Feynman's approach to quantum mechanics (and quantum field theory), called "Euclidean Quantum Mechanics". The last European postdoc, M. Thieullen (from Paris VI), working together with J.C.Zambrini, has produced during her H.C.M. fellowship in Lisbon two publications, one to appear in P.T.R.F. (ref.2) and another to appear in Ann.I.H.P., sec. Phys. Theor. (ref.3) . The spirit of this program is, therefore, resolutely interdisciplinary (Probability theory and theoretical Physics) and should attract candidates motivated more by innovative applications of stochastic analysis then by improvements of familiar ideas and techniques.
The scientific environment at the research institute is favourable. We have many foreign visitors during the academic year, coming from all over the world, active groups of research in PDE, Geometry and other fields, and our experience with postdocs has been, up to now, perceived quite positively by them. In addition, Lisbon is an interesting city, rich in history, where visitors enjoy a different lifestyle.
References:
[1] A.B.Cruzeiro and P.Malliavin _"Renormalized differential geometry on path space: structural equation, curvature", J.Funct.Anal,v.139, 1996,p.119-181
[2] M.Thieullen and J.C.Zambrini _"Symmetries in stochastic calculus of variations", to appear in Prob.Th. and Related Fields
[3] M.Thieullen and J.C.Zambrini _"I. The
theorem of Noether in Schroedinger's Euclidean quantum
mechanics", to appear in Ann.Inst. Henri Poincare