This programme finished its activities in September 2004
Main pages of Institute of Mathematics,
Stefan Banach International Mathematical Centre,
Mathematical Conference Centre in Będlewo.
Project Coordinator:
Prof. Feliks Przytycki
Objectives:
The Centre of Excellence will stimulate and coordinate research and
activities at the border of pure mathematics and applications, as well as to
stimulate interdisciplinary research.
What is lacking in Poland (and also in other preaccession phase countries),
it is a link between
pure research and applications. It is a general trend in world
(especially in highly developed countries), to eliminate middle stages
between pure sciences and applications. More and more
often the so-called "pure scientists" could communicate with people from the
very application process. Unfortunately, such approach falls very short in
Poland. It is mostly due to inheritance of communism, which destroyed
enterprise and competitiveness culture at the borderline between sciences and
industry and it is our aim to re-establish with EU help such relations in the
field of mathematical sciences, and to employ mathematics to needs of the
society.
Description of work
Activities will be divided into eight packages:
- Public-Key Cryptography and Computational Number
Theory
- Information Theory and its Applications to Physics,
Finance and Biology
- Mathematical Modelling and Analysis of Cellular
Populations
- Nonlinear Systems and Control
- Mathematics of Finance and Stochastic Control
- Approximation structures in Banach spaces
- Symplectic Singularities and Applications
- Visual Modelling
Each topic will last between twelve and twenty four months. Forms of
activities will include
- cooperative research in above listed novel, and important topics,
together with invited foreign scientists. Those projects will also exploit
existing links with analogous institutes, including
Max-Planck-Institut für Mathematik in Bonn,
Institut des Hautes Etudes Scientifiques in Paris,
Erwin Schrödinger International Institute for Mathematical
Physics in Vienna,
Mittag-Leffler Institute in Djursholm,
Centre International de Rencontres Mathematiques in Marseille,
and several first class universities. Such activities should attract bright
young people and also help to establish collaboration with more applied
research;
- organisation at the Banach Center of international conferences,
workshops, semesters, research groups, schools for young researchers.
We expect that our approach, following established tradition of the Banach
Center, will bring new qualitative and quantitative results, both in pure and
applied mathematics. Activities at the Center, including such important
topics like elliptic curves cryptosystems, new algorithms for wavelet
compression techniques, stochastic analysis of financial derivatives, risk
theory, multi-scale biological visual modelling should have long lasting
impact, contributing to our knowledge, and increased intellectual potential.
Should also bring new impulses for modern technology based on applied
mathematics.
We expect several mathematicians to take part in realization of the program
of the Centre, including distinguished specialists as well as
post-doctorate researchers.
Core for European Excellence Networks
(agreement between the Institutes of Mathematics of the Academies
of Bulgaria, Hungary, Poland and Romania
Work packages progress report:
Dec. 2000 - May 2003,
as Word document
Package 1.
Public-Key Cryptography and Computational Number Theory
Start: December 2000
Timetable:
1) Invitation of specialists in the field during December 2000 - November
2001
2) Organization of a workshop -
11 - 15 June 2001
3) Organization of a conference - November 2001
Coordinator: Jerzy Urbanowicz
Objectives:
Development of faster encryption algorithms with shorter keys and lower
memory and processing power requirements for smart cards applications.
Analysis of provable security protocols for new cryptosystems based on
elliptic curves and group algebra and better understanding of underlying
mathematics to assure a high cost of cipher-breaking.
Description of the contents, the workplan, the steps, the approach or
the methodology:
Cryptographic technologies are at the heart of information society. The rapid
growth of Internet and electronic commerce in Europe is directly related to
widespread use of cryptography as the preferred means to ensure authenticity
and confidentiality in electronic communications.
However, despite more than 50 years of mathematical cryptography, there is no
publicly known complete mathematical proof of strength for any practical
cipher. Also, despite rapid development of cryptography for practical
applications there are only very few mathematicians involved in cryptography
studies in Central Europe. We propose to enhance both the research in the
field and multilateral interaction in the Central Europe region using the
Centre of Excellence as a platform initiating, stimulating and proliferating
cryptography research. We plan to organise a mini-school of cryptography for
young researchers from Central Europe and to give them an opportunity to work
together with, and to listen lectures by prominent European experts in the
field and representatives of the industry using cryptography for electronic
trade and banking. The Centre will promote new ideas and will help young
scientists to transfer their results into commercial applications. The Centre
will also, by public lectures and open panel discussions, attempt to increase
a general cryptography literacy level of various professional groups (medical
doctors, lawyers, banking and insurance industry professionals, etc.) and
high school students. The conferences, devoted to "The mathematical aspects
of public key cryptography" is planned.
Partners involved:
- H. Niederreiter (Institute of Discrete Mathematics, Vienna, Austria)
- G. Frey (Institut für Experimentelle Mathematik, Universität
Essen, Germany)
- J. Brzezinski (Department of Mathematics, Chalmers Univ. of Technology,
Göteborg, Sweden)
Package 2.
Information Theory and Applications to
Physics, Finance and Biology
Type of activity: workshop, conference, research visits
Start: December 2000
Timetable:
Activity for this package occupies months December 2000 - November 2002
Information Theory Days,
23 -29 April 2001
Conference Applications of Information
Theory in Biology, Finance and Physics -
21 - 26 May 2001
Workshop Information Theory, Algorithms and Applications to Probability
and Statistics - 15 - 20 October 2001
Workshop Holomorphic
Iteration, Non-uniform Hyperbolicity, 22 - 25 May,
Warszawa
Coordinators:
Flemming Topsøe,
Feliks Przytycki
Objectives:
- to introduce young researchers to new developments in Information Theory
with a special view to applications in Physics, Finance and Biology; this
especially involves the Polish scientific community - which at present only
has little activity and expertise in the area,
- research in an international setting with key
specialists visiting, instructing at a workshop and lecturing at the
conference which will mark the close of the activity.
Description of the contents, the workplan, the steps,
the approach or the methodology:
The purpose of the activity is to combine two approaches to the information
theory, the one based on universal coding and prediction developed by the
Russian, Israeli, American and other schools with another game theoretical
approach. It is expected to obtain applications to cryptoanalysis, parts of
quantum physics, finance theory (e.g. portfolio management), statistics, and
biology.
An international conference will be held in May.
A further major meeting is expected in
October. Extended studies at the Banach Center will also take place.
For further details, we refer to
https://www.math.ku.dk/IT-Banach2001
Partners involved:
- Mark Broom (Sussex, BIOLOGY)
- Imre Csiszar (Budapest, INFORMATION THEORY)
- Denes Petz (Budapest, QUANTUM INFORMATION THEORY)
- Zhanna Reznikova (Novosibirsk, BIOLOGY)
- Boris Ryabko (Copenhagen, UNIVERSAL CODING, INFORMATION THEORY)
- Dominick Samperi (New Yourk, FINANCE THEORY)
- Lukasz Stettner (Warsaw, Director of the Banach Centre)
- Flemming Topsoe (Copenhagen, INFORMATION THEORY)
- Igor Vajda (Prague, STATISTICS)
Package 3.
Mathematical Modelling and Analysis of Cellular Populations
Type of activity: research visits, conference, workshop
Start: June 2002
Timetable: 14 months,
School on Population Dynamics, Będlewo, Poland, June 17 - 21, 2002
Conference on Mathematical Modelling of Population Dynamics, Będlewo, Poland, June 24 - 28, 2002
Coordinator: Ryszard
Rudnicki
Objectives:
- Mathematical description of theoretical functions of population
dynamics.
- Qualitative properties of cellular populations: stability, periodicity,
chaos.
- Application to periodic hematological diseases and tumor growth
control.
Description of the contents, the workplan, the steps, the approach or
the methodology:
The aim of our project is to build mathematical models describing theoretical
foundations of population dynamics and study them to obtain qualitative and
quantitative properties of populations. The main object of our study are
bacteria populations, blood cells and tumour cells. The crucial role in the
description of these populations is played by the cell cycle. A single cell
is characterized by its maturity (or biological age) which governs the life
history of any cell. Physiologists associate the maturation with the size of
the cell or with the concentration of a special substance. Models of this
type have been yet studied but it has been assumed that reproduction occurs
by fission into two equal parts.
This assumption is only a simplification of the real process of replication
because it does not take into consideration the stochastic character of the
distribution of maturation into daughter cells. We want to study models
based on the hypothesis that the maturity of the daughter cells is described
by means of the probabilistic measure which depends on the maturity of the
mother cell.
The biological assumptions on rates of division, mortality and maturity
growth lead to complicated partial differential equations with integral
perturbation. Our team has developed some methods of study of equations of
this type. In particular methods based on the spectral analysis and the
theory of Markov semigroups lead to interesting mathematical and biological
results as asymptotic stability or chaotic behaviour of the population. Our
research is inspired by new trends and results of theoretical biology. We
want to apply our results to study periodic haematological diseases and to
tumor growth control.
Partners involved:
- Prof. Ovide Arino, Laboratoire de Mathématiques Appliquées,
Université de Pau, Pau, France,
- Prof. Odo Diekmann, Utrecht University, Utrecht, The Netherlands,
- Prof. Eva Sánchez, Departamento de Matemática Aplicada,
E.T.S. Ingenieros Industriales, Madrid, Spain,
- Laurent Pujo-Menjouet, Laboratoire de Mathématiques Appliquées,
Université de Pau, Pau, France,
- Dr. N.E. Elhoussif, Utrecht University, Utrecht, The Netherlands.
Also Prof. M.C. Mackey, McGill University, Montreal, Canada
will participate in the project.
Package 4.
Banach Center Semester on Nonlinear Systems and Control
Type of activity: workshop, Ph.D. courses, conference, research visits
Start: December 2002
Timetable:
1. Invitation of specialists in the field during December 2002 - November
2003
2. Preparatory courses for Ph.D. students or young researchers, introducing
main tools - December 2002 - February 2003
3. A workshop, survey and expository lectures presented by best specialists
in the field
4. Research seminars and research on new results/techniques presented during
the workshop
5. A specialized conference focused on the most active areas of the research
Coordinator: Bronisław
Jakubczyk
Objectives:
Introducing the techniques offered by recent advances in nonlinear system and
control theory to candidates for researchers and to young researchers.
Emphasis on applications. Improving techniques of stabilization (static and
dynamic), observability and observers, optimal control and feedback
modification. Applications in robotics, batch reactors, destilation columns,
biological systems.
Description of the contents, the workplan, the steps, the approach
or the methodology:
In the first part we intend to organize a summer school consisting of 3-4
parallel advanced mini-courses which will give an introduction to the
subject and present basic techniques and results which were obtained during
last 10-20 years.
Topics covered in the courses should include: controllability, observability,
realization theory, stabilization, adaptive control, filtration, feedback
equivalence and linearization, decoupling and disturbance decoupling, optimal
control and examples of applications, nonholonomic systems, systems appearing
in robotics, aerospace engineering, chemistry and biology.
The second part of the semester is intended to gather
specialists working in the field of nonlinear system
theory and control theory, and in areas where applications of this field
appear. In the last month a conference is planned.
Partners involved:
- Bernard Bonnard, Departement de Mathématiques, Université
de Bourgogne, Dijon
- Witold Respondek, Institut National des Sciences Appliquees de Rouen,
Rouen
- Michael Zeitz, University of Stuttgart, Institut für Systemdynamic
und Regelungstechnik
Package 5.
Finance Mathematics and Stochastic Control
Type of activity: workshop, summer school, research visits
Start: June 2001
Timetable: 12 months
1. Invitation of specialists in the field during 12 months period,
2. International Workshop on Mathematics of
Finance01School.htm - June 4-10, 2001,
3. Summer School on Mathematics of
Finance - July 2-10, 2001,
4. International Workshop on Stochastic Control and its Applications
- June 3-8, 2002.
Coordinator: Łukasz
Stettner
Objectives:
The purpose of the project is to stimulate research on the following topics:
- pricing of financial derivatives on incomplete market models,
- analysis of term structure models,
- construction of models with risk,
- application of stochastic control in mathematics of finance,
- asymptotic properties of stochastic control models.
A special attention will be devoted to educate young mathematicians in
direction of mathematics of finance on various levels: Ph.D.'s in mathematics
of finance, lecturers ready to teach mathematics of finance.
Description of the contents, the workplan, the steps, the approach
or the methodology:
We plan to organize first two international workshops. The first one
on recent developments in mathematics of finance, in particular:
on martingale and stochastic control methods in pricing of financial
derivatices, term structure models and stochastic partial differential
equations corresponding to these models. The second workshop will be devoted
to stochastic control methods and their applications with an emphasis on
mathematics of finance (in particular the study of various risk cost
functionals).
The purpose of a summer school on mathematics of finance is to give a number
of lectures how to teach mathematics of finance. It is expected to invite
5-6 lecturers who
are experienced in teaching mathematical finance, and will be able to deliver
series of selfcontained lectures as well as to share their teaching
experiences. The following series of lectures are considered: static
portfolio analysis (Markowitz theory), dynamic portfolio selection models -
Bellman equations, introduction to pricing of financial derivatives in
discrete time, stochastic calculus and Blacke-Scholes model, term structure
models, financial engineering.
Partners involved:
- from Italy: professors: W. Runggaldier, G.B. Di Masi,
P. Dai Pra from Padova, M. Frittelli from Milano,
G. Da Prato and Prattelli from Pisa,
- from France: professors: A. Sulem, Y. Kabanov (Besançon),
N. Touzi, H. Pham, N. El Karoui from Paris VI,
E. Jouini from ENSAE,
- from Germany: professors: K. Helmes and M. Schweizer from Berlin,
M. Kohlmann from Konstanz, U. Rieder from Ulm, M. Schal
from Bonn,
- from the Netherlands: prof. A. Bagchi from Twente.
Package 6.
Approximation Structures in Banach Spaces
Type of activity: workshop, conference, research
Start: December 2001
Timetable: 24 months
1. Invitation of specialists in the field
2. Workshop for graduate students
3. International Conference
Coordinator: Przemysław Wojtaszczyk
Objectives:
Many topics in functional analysis like bases in Banach spaces, local theory
or theory of s-numbers provide a conceptual basis for many applied or
computational methods. As examples let us mention theory of computational
complexity, wavelet methods for signal compression and analysis or Gabor
analysis. The objective of the program is to provide a framework and
opportunity for interaction of researchers in those fields of functional
analysis with specialists in numerical or computational fields.
Description of the contents, the workplan, the steps, the approach
or the methodology:
The aim of the program is to show to the pure functional
analyst that his field of research has close ties with many applied theories
and those theories may serve as great source of important questions.
Quantitative estimates of geometry of convex bodies which are essential to
local theory of Banach spaces (like various s-numbers, projection
constants etc.) have also direct bearing on estimates of computational
complexity or efficiency of numerical algorithms, especially non-linear.
Various bases in Banach spaces like wavelet bases, spline bases, polynomial
bases, Walsh and trigonometric systems form a foundation of various numerical
methods. Especially important are trash-holding methods for data analysis
and compression based on wavelet bases. The fact that those bases are
unconditional bases in many function spaces ensures the great efficiency of
those algorithms. This connects numerical methods, functional analysis and
function theory. On the other hand ridge approximation which is an active
area of research in function theory and is directly motivated by computer
tomography and neural networks should lead to important questions in
functional analysis.
Partners involved:
- prof. Stephane Jaffard (Paris)
- prof. Gilles Pisier (Paris VI)
- prof. S.J. Szarek (Paris and Cleveland)
- prof. Hermann König (Kiel)
- prof. Stephan Heinrich (Kaiserslautern)
- prof. Wolfgang Lusky (Paderborn)
- prof. Bernd Carl (Jena)
- prof. Wolfgang Sickel (Jena)
- prof. Hans Feichtinger (Wien)
- prof. Paul Müller (Linz)
- prof. O. Christiansen (Denmark)
- prof. J. Garcia-Querva (Universidad Autónoma de Madrid)
- prof. Gustav Gripenberg (Helsinki)
Package 7.
Symplectic Singularities and Applications
Type of activity: workshop, conference, research visits
Start: December 2001
Timetable: 24 months
1. Invitation of specialists in the field
2. Workshop
3. Conference
Coordinator: Stanisław
Janeczko
Objectives:
Formulation of a new approach to the collective phenomena, braking of
symmetry. Classification of symplectic spaces and structures.
Description of the contents, the workplan, the steps, the approach
or the methodology:
Classification of caustic invariant with respect to the compact symmetry
group action;
Finding of symplectic invariants of systems of surfaces and composed
symplectic relations;
Recognition of integrability of the implicit differential systems -
generalized Hamiltonian dynamics;
Diffraction patterns and extension of A, D, E classification of simple
singularities;
Application of modern symplectic topology results and techniques -
Gromov-Witten invariants.
Extension of pseudoholomorphic curves methods to the singular symplectic
structures.
Partners involved:
H. Farkas, Technical University of Budapest;
P. Giblin, J.W. Bruce, University of Liverpool;
J.C. Sikorav, Ecole Normale Superieure Lyon;
Dierk Siersma, Utrecht Univ.
Package 8.
Visual Modelling
Type of activity: workshop, conference, research visits
Start: December 2000
Timetable:
1) Invitation of specialists in the field - December 2000 - May 2002
2) Organization of a workshop - May 2001
3) Organization of a conference - April 2002
Coordinator: Marek Niezgódka
Objectives:
Facilitating the researchers participating in the project to verify their
solutions in a distributed visual modelling environment with the use of
advanced computing infrastructure.
Description of the contents, the workplan, the steps, the approach
or the methodology:
Computational resources and expertise of
ICM
will be used for development of
visual modelling environments for various field of application oriented
research, including biomolecular, atmospheric and medical science. The
developed solutions form an extensive set of numerical, programming and
visualization tools that can be used for conducting, verifying and analyzing
of mathematical and numerical models of complex, multi-scale physical,
biological and economical systems. ICM plans to allow the participants of
the project the access to these resources by:
- Organization of a workshop in visual modelling
- Assigning a staff member for consulting work
- Assigning necessary computational and network resources
- Organizing a conference summarizing developments of the project
- Inviting several specialists for lectures, workshops and cooperative
work
- Creation of an integrated, distributed visual programming environment
for rapid prototyping of algorithmic solutions
Partners involved:
1. IWR (Interdisciplinary Scientific Computing Centre), University of
Heidelberg
2. Institute of Applied Mathematics, University of Freiburg
