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Banach Center

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.

Algebra,    Geometrie und Topologie

University of Gdansk, Gdansk University of Technology

Email: gwgt@ug.edu.pl

'The Mathematical Research and Conference Center, Institute of Mathematics of the Polish Academy of Sciences'

Interactions between algebraic, asymptotic and enumerative combinatorics is the central theme of the summer school. Our aim is to provide a platform for keen researchers to delve into these research areas, guided by the lectures of the invited specialists.

The summer school is intended for young researchers working in algebraic, asymptotic and enumerative combinatorics or who would like to deepen their knowledge. Of course, more mature researchers are also most welcome.

The main content of the summer school is provided by three series of lectures by the three invited speakers who are experts in these fields of research. Each series consists of 5 lectures (60 minutes each) accompanied by 2 exercise sessions (60 minutes each).

Junior participants will have an opportunity to present posters. There will be a limited number of short talks which are intended as a possibility for junior participants to present their results.