And here comes the next KSE Mathematics Seminar:
 
“Automatic sequences from the point of view of higher order Fourier analysis”
 
Speaker: Jakub Konieczny (Kyiv School of Economics)
 
🗓When: February 11, 16:30–17:30
📍Where: KSE Dragon Capital Building, 3 M. Shpaka St., Room 4.07

Abstract:
Automatic sequences give rise to one of the most basic models of computation and have remarkable links to various areas of mathematics, including dynamics, algebra and logic. Many properties of these sequences have been extensively studied. In my talk, I will focus on the perspective of combinatorial number theory, or more specifically - higher order Fourier analysis. Together with Jakub Byszewski and Clemens Müllner we obtained a decomposition result which allows us to express any (complex-valued) automatic sequence as the sum of a structured part, which is easy to work with, and a part which is pseudorandom or Gowers uniform. This has immediate applications to the asymptotic count of additive patterns, as well as less direct application to arithmetical subword complexity (joint with Müllner) and quantitative variants of Cobham's theorem (upcoming paper with Adamczewski and Müllner).