Aktualności CB
Upcoming conferences
1) NUMBERS IN THE UNIVERSE: recent advances in number theory and its applications 7-11 August 2023
Number theory mixes techniques from various branches of mathematics and reveals unexpected connections between them. The first conference organised by the International Centre for Mathematics in Ukraine aims to overview recent breakthroughs in this field.
The event will take place simultaneously in two grounds with a live connection between the audiences at The Kyiv School of Economics and Stefan Banach International Mathematical Center in Warsaw. Students and young scientists are encouraged to take part. There will be special sessions organised to discuss research and learning problems stated by the speakers.
LECTURE SERIES
- Vitaly Bergelson, The Ohio State University, Ergodic theory at the service of combinatorics and number theory
- Terence Tao University of California, Los Angeles, Analytic prime number theory in the twenty-first century
- Maryna Viazovska, École Polytechnique Fédérale de Lausanne, Old and new ideas in sphere packing
INVITED SPEAKERS
- Joanna Kułaga-Przymus, Nicolaus Copernicus University, Toruń
- Mariusz Lemańczyk, Nicolaus Copernicus University, Toruń
- Oleksandr Marynych, Taras Shevchenko National University of Kyiv
- Danylo Radchenko, University of Lille/CNRS
- Fernando Rodriguez Villegas, The Abdus Salam International Centre for Theoretical Physics, Trieste
2) High Dimensional Probability 11 - 16 June 2023 | Będlewo
High Dimensional Probability has its roots in the investigation of limit theorems for random vectors and regularity of stochastic processes. It was initially motivated by the study of necessary and sufficient conditions for the boundedness and continuity of trajectories of Gaussian processes and extension of classical limit theorems, such as laws of large numbers, laws of the iterated logarithm and central limit theorems, to Hilbert and Banach space-valued random variables and empirical processes.
It resulted in the creation of powerful new tools - the methods of high dimensional probability and especially its offshoot, the concentration of measure phenomenon, were found to have a number of applications in various areas of mathematics, as well as statistics and computer science. These include random matrix theory, convex geometry, asymptotic geometric analysis, nonparametric statistics, empirical process theory, statistical learning theory, compressed sensing, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, random graph theory, as well as information and coding theory.
The aim of this workshop is to bring together leading experts in high dimensional probability and a number of related areas to discuss the recent progress in the subject as well as to present the major open problems and questions. We want to deepen contacts between several different communities with common research interests focusing on stochastic inequalities, empirical processes, strong approximations, Gaussian and related chaos processes of higher order, Markov processes, concentration of measure techniques and applications of these methods to a wide range of problems in other areas of mathematics, statistics and computer science. We would also like to foster and develop interest in this area of research among new researchers and recent Ph.D.'s. There are many exciting open problems in the area that may be formulated in a way that can be understood by graduate students. We hope that they will attract attention of young people taking part in this workshop.
Particular areas of focus and interest for the meeting include:
- Application of generic chaining techniques to study the regularity of stochastic processes and lower and upper bounds on norms of random vectors and matrices
- Relation between various isoperimetric and concentration inequalities as well as their applications to convex geometry, statistics and computer science
- Applications of modern empirical process and strong approximation methods to problems of machine learning and inference in high- and infinite-dimensional statistical models
- Interactions between information-theoretic inequalities, convex geometry and high-dimensional probability
- Stein’s method and its use in high-dimensional probability
- Nonasymptotic random matrix theory and applications to quantum information theory
- Interactions between high dimensional probability and statistical physics
- Super-conconcentration phenomena in high dimension: new tools, examples and open problems
- Application of Itô calculus to convex geometry
- Identification of major problems and areas of potentially high impact for applications and use in other areas of mathematics, statistics, and computer science
Scientific Committee
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Nathael Gozlan
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Mokshay Madiman
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Florence Merlevède
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Elisabeth Werner
3) Nilpotent structures in topological dynamics, ergodic theory and combinatorics 04 - 10 June 2023 | Będlewo
Aims and Scope
Classical Fourier analysis uses decompositions of functions in terms of linear phases. In recent years it was discovered that for applications in ergodic theory, combinatorics, and number theory, involving patterns such as arithmetic progressions, one has to study correlations of functions with higher order polynomial phases and other more general phases, called nilsequences, which arise from natural dynamical systems on nilmanifolds. This philosophy has helped to make progress in problems that were previously considered intractable, and has resulted in new impressive applications in the above-mentioned areas. In ergodic theory this approach is used to study the limiting behavior of multiple ergodic averages and related multiple recurrence results, in topological dynamics it has led to new structural results, and in combinatorics and number theory it is used to study patterns that can be found in sets of positive density or the set of primes. Also, very recently it has played a decisive role in progress related to the Chowla and Elliott conjectures on correlations of bounded multiplicative functions and the Mobius disjointness conjecture of Sarnak. The aim of the workshop is to introduce the above topics to a wider audience, report on recent developments, and foster collaborations and new insights.
Outline of the conference
The conference will start with a mini-course by the organizers on background material related to nilpotent structures and their applications, emphasizing a recent robust approach to nilsequences via the notion of nilspaces.
The conference will continue with talks given by the participants on various aspects of the theory including applications and related topics.
Scientific Committee
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Vitaly Bergelson, Ohio State University
Bernard Host, Université Paris-Est - Marne-la-Vallée
Bryna Kra, Northwestern University
Mariusz Lemańczyk, Nicolaus Copernicus University in Toruń
Other news
Meeting of the Scientific Council of the Banach Center will be held on 19-20 May 2023.
The International Scientific Council of the Banach Center is a prestigious advisory body, consisting of distinguished Polish and European mathematicians nominated by IMPAN and by the European Mathematical Society. The Council is primarily responsible for evaluating and promoting the scientific programme of the Banach Center. The members meet every year in Spring in Warsaw in order to evaluate the submitted proposals and discuss the future programme; this time the meeting takes place on the 19th-20th May.
