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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.

Geometry and Topology,    Graph Theory and Combinatorics

Banach Center

LOOPS'23 conference will belong to the LOOPS conferences, a series of conferences held every 4 years since 1999. The LOOPS conferences cover all aspects of nonassociative mathematics, including quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, quandles and their applications. The conference intends not only to highlight new relevant results in algebra and geometry, but also to foster connections to combinatorics, group theory, knot theory, cryptography and physics. The previous LOOPS conferences have been held in Prague, in Trest, Czech Republic, Ohrid, North Macedonia, and Budapest, Hungary.

quasigroups and loops • quantum Latin squares • applications in cryptography • automated deduction • algebraic structures derived from the Yang-Baxter equation • connections to low-dimensional topology

Jagiellonian University

Cracow Logic Conference (CLoCk) is the oldest Polish conference series on logic. For many years it existed under a deceptive name Konferencja Historii Logiki (Conference on the History of Logic). The present conference in 68th in the series.

Organisers (Dept. of Logic);     Email: dlg@iphils.uj.edu.pl

algebraic logic, model theory, proof theory, philosophical logic

Mathematical Logic and Foundations,    History and Philosophy of Science and Technology

Geometry and Topology,    Number Theory, Arithmetic

Institute of Mathematics – Polish Academy of Sciences