Following the EU grant to Stochastic Analysis under Framework IV (ERBFMRXCT960075), applications are invited for two fellowships tenable within the participating research teams of the following mathematical departments:
Closing date: 30 September 1997.
Duration: Negotiable, from 6 to 24 months for each
fellowship.
The fellowships are open for young, mainly post doc, researchers, although there are possibilities also for PhD students. Ideally, the candidates have a background in stochastic analysis and differential geometry.
More details on eligibility, etc., can be found on local documents concerning the previous (first) application period and on the original corresponding documents at the web site of the project.
Applications should be sent to the scientists in charge of the respective institutions, including full curriculum vitae with age and nationality, list of publications, and a short account of research interests and achievements. The application should also include names and full addresses of three academic referees. Applicants must specify preference for host institution, and are required to ask their referees to write directly to the scientist in charge of the relevant institution.
A copy of the application should also be sent to the coordinator:
Prof. Terence John LyonsInformation of a general scientific nature relating to the project, as well as more detailed scientific information, can be found on this site, and on the Project home page.
Among the research areas we mention:
There are also possibilities for research in areas bordering to stochastic analysis, e.g. differential geometry and Schrödinger operators.
The fellows are expected to participate in work carried out jointly by the two institutions.
The Group of Mathematical Physics of the University of Lisbon is presently interested in two interrelated directions of research in stochastic analysis:
It has been shown recently, in the study of path spaces, that a renormalization of the geometrical objects using Itô's theory of integration allows one to construct a new type of geometry in infinite dimension. This applies, for example, in the theory of path integrals on Riemannian manifolds, used formally in theoretical physics.
[1] P. Malliavin, "Stochastic Analysis",
Grund. der Math. Wis. 313 (Springer, 1997).
[2] A. B. Cruzeiro and P. Malliavin,
"Renormalized differential geometry on path space: structural equation,
curvatures", J. Funct. Anal. 139 (1996), 119-181.
[3] A. B. Cruzeiro and S. Fang, J. Funct. Anal.
143 (1997), 400-414
Although the probabilistic content of elementary quantum mechanics is poor, a probabilistic analogy developed in the past 12 years under the name of Euclidean quantum mechanics (EQM) allows one to use stochastic analysis for discovering new theorems relevant to quantum mechanics. Reciprocally, it injects into stochastic analysis new ideas inspired by quantum physics. Recently, the existence of a theorem of Noether in EQM has been shown in this way, using tools of stochastic analysis. The corresponding new quantum theorem is richer than its Hilbert space counterparts.
[0] T. Kolsrud and J. C. Zambrini, "The general mathematical
framework of Euclidean quantum mechanics: an outline", in
A. B. Cruzeiro and J. C. Zambrini (eds.),
Stochastic Analysis and Applications, Progress in
Prob. Series 26 (Boston: Birkhäuser, 1991).
[1] M. Thieullen and J. C. Zambrini,
"Symmetries in stochastic calculus of variations",
to appear in Prob. Th. and Related Fields (1997).
[2] M. Thieullen and J. C. Zambrini, "Probability
and quantum symmetries. I. The theorem of Noether in Schrödinger's
Euclidean quantum mechanics", to appear in Ann. Inst. Henri
Poincaré (Phys. Théor.) (1997).
[3] T. Kolsrud, "Quantum constants of motion and the heat Lie algebra
in a Riemannian manifold", Stockholm Preprint, submitted (1996).
GFM
<gfm@alf1.cii.fc.ul.pt>,
JMCE
<jmce@titania.cii.fc.ul.pt>
URL:
http://alf3.cii.fc.ul.pt/gfm/Jobs_grants/SA_TMR_fellowships-2.en.html
Last modified: Mon Feb 3 21:10:47 WET 1997
