Nilpotent Structures in Topological Dynamics, Ergodic Theory and Combinatorics

29 Aug - 04 Sep 2021Add To Calendar
Będlewo, Poland
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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 .. continue reading 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.


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The Mathematical Research and Conference Center

Poland10 Total Events / 8 Upcoming Events

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