PHD · Phenomena in high dimensions
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2004-11-01 → 2008-10-31
- EU contribution
- €1,756,002
- Participants
- 13
- Scheme
- RTN
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Results in brief
Final Activity Report Summary - PHD (Phenomena in high dimensions)
This project brought together internationally leading researchers and young scientists from several mathematical disciplines - probability theory, high-dimensional geometry, combinatorics and mathematical physics - to focus jointly on the remarkable phenomena that arise in high-dimensional systems. The analysis of such complex systems plays, and will continue to play, a major role in the development of many scientific areas in the coming decades, including physics, biology and economics. The areas of mathematics represented in the project have, until recently, been considered quite separate: but they have developed a commonality of methods and viewpoints because of the appearance in all of them of pseudo-random phenomena, created by the high-dimensionality. Once a system becomes sufficiently complex, it is impossible (and probably not very useful) to predict the detailed nature of small-scale features of it. On the other hand, crucial features of its large-scale behaviour often become predictable because its complexity forces it to mimic random behaviour: behaviour generated by the interaction of many independent effects. The project combined ground-breaking scientific research with the training of a new generation of young mathematicians who have acquired a familiarity with all or many of the different strands of high-dimensional mathematics. The research outcomes include: - a rigorous derivation of the formula for the energy of spin-systems of sub-atomic particles; - faster algorithms (based on carefully designed random sampling) for the calculation of parameters associated to high-dimensional objects; - a rigorous demonstration of the existence of a universal pattern in the distribution of the characteristic frequencies of matrix models; - a new formula for the measure of disorder in random systems that can be used for effective computation; - a more detailed explanation of how high-dimensional geometry automatically produces characteristically random effects; and - a subtle new way to describe large networks by encoding their local properties in a single 'landscape'.
Data: CORDIS, © European Union
Project objective
This programme will bring together internationally leading researchers and young scientists from several mathematical disciplines. The goal of the project is to investigate and to understand in depth the typical phenomena that occur in high-dimensional sy stems. The multidisciplinary program will provide young scientists with an appreciation of the unity of these disciplines and will structure their research training to help them freely to transfer ideas from one context to another. The achievement of t his goal will be facilitated by the fact that among the senior scientists in the programme are many of the architects of the last 20 years¿ developments. Each year there will be an annual one-week conference and summer schools lasting one or two months, where students and postdoctoral researchers will be able to meet, to talk to leading figures in several different fields, and to attend expository lecture courses. The network will also organize one or more shorter workshops each year, on specific topics w ithin the programme, where the emphasis will be on training and transfer of knowledge. There will be an annual 2-3-day workshop in which fellows will be asked to present their work and to attend the presentations of others. The six main task areas of the project are : ¿ Asymptotic Geometric Analysis ¿ Isometric Convex Geometry ¿ Asymptotic Combinatorics ¿ Randomised Computation and Complexity ¿ High-dimensional Phenomena in Mathematical Physics ¿ Isoperimetric Principles in Geometry and Probability The co ordinator and the Mathematical Department of Marne-la-Vallée will provide appropriate support for network information centre including a web homepage, newsletters and a preprint database in order to ensure effective dissemination of the results. The netwo rk contains 13 participants from 11 countries and involves more than 300 researchers. It will provide a minimum of 285 person-months of training for Early Stage and Experienced Researchers.
Original text from CORDIS.
Participants
- CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE · PARISCoordinatorFrance
- ALFRED RENYI INSTITUTE OF MATHEMATICS - HUNGARIAN ACADEMY OF SCIENCES · BUDAPESTHungary
- Albert-Ludwigs-Universität Freiburg · FreiburgGermany
- CHRISTIAN-ALBRECHTS-UNIVERSITÄT ZU KIEL · KIELCity levelGermany
- INSTITUTE FOR LOW TEMPERATURE PHYSICS · KHARKOVCity levelUkraine
- INSTITUTE OF MATHEMATICS OF THE POLISH ACADEMY OF SCIENCES · WARSAWCity levelPoland
- NATIONAL AND KAPODISTRIAN UNIVERSITY OF ATHENS · ATHENSGreece
- TEL AVIV UNIVERSITY · TEL AVIVIsrael
- Technische Universität Wien · WienAustria
- UNIVERSIDAD DE ZARAGOZA · ZARAGOZASpain
- UNIVERSITA DEGLI STUDI DI FIRENZE · FIRENZEItaly
- UNIVERSITE PAUL SABATIER-TOULOUSE III · TOULOUSEFrance
- UNIVERSITY COLLEGE LONDON · LONDONUnited Kingdom
Links
Data: CORDIS, © European Union