Conférences  >  Mathématiques  >  Géométrie et topologie  >  Pologne

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.

Algèbre,    Théorie des graphes et combinatoire

Banach Center

Banach Center

This conference is a celebration of the mathematical career of Szymon Dolecki, representing advances in the various fields he contributed to: Control Theory and observability (main speaker: Enrique Zuazua), Optimization (main speaker: Jean Paul Penot), Topology (main speakers: Alexander V. Arhangel’skii, Ahmed Bouziad, Jean Goubault-Larrecq, Steve Watson), as often as possible from the point of view of the unifying theme of convergence space theory (workshop leader: Frédéric Mynard), a domain of which he is one of the most prominent world specialist and that centrally occupied the later part of his career.

Banach Center

The conference concerns the broadly understood mathematical analysis, in particular, the so-called geometric analysis (including calculus of variation and partial differential equations of geometric origin, Sobolev spaces theory on manifolds and on metric spaces, and knot theory issues related to curvature energies).

Analyse,    Calcul infinitésimal, équations différentielles et intégrales