Join the KSE Mathematics Seminar on the topic “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).

About the Speaker:

Jakub Konieczny is a Simons Professor of Mathematics at KSE. He specializes in combinatorial number theory, particularly in applications of ergodic theory. Jakub earned his PhD from the University of Oxford in 2017. Following his doctoral studies, he held postdoctoral positions at the Hebrew University of Jerusalem (2017–2020) and the University of Lyon (2020–2023). Prior to joining KSE, he served as a Senior Research Associate at the University of Oxford.

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Looking forward to seeing you there!