### Program v akademickém roce 2019/2020

22. 1. 2020

W. Mance (Adam Mickiewicz University in Poznań, Poland), Normal numbers for the Cantor series expansion and possible applications in algebraic geometry.

Abstract: We will discuss basic properties of normal numbers for the Cantor series expansions and a recent result of D. Airey and B. Mance. Using ideas introduced in this paper, it may be possible to show that information about algebraic varieties is encoded in the structure of sets of normal numbers. We will outline this idea and the barriers one may encounter in finishing it.

15. 1. 2020

W. Mance (Adam Mickiewicz University in Poznań, Poland), Borel complexity of sets of normal numbers via generic points in subshifts with specification.

Abstract: We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $b$ expansions, and their various generalisations: generalised L{\"u}roth series expansions and $\beta$-expansions. In fact, we consider subshifts over a countable alphabet generated by all possible expansions of numbers in $[0,1)$. Then normal numbers correspond to generic points of shift-invariant measures. It turns out that for these subshifts the set of generic points for a shift-invariant probability measure is precisely at the third level of the Borel hierarchy (it is a $\Pi^0_3$-complete set, meaning that it is a countable intersection of $F_\sigma$-sets, but it is not possible to write it as a countable union of $G_\delta$-sets). We also solve a problem of Sharkovsky--Sivak on the Borel complexity of the basin of statistical attraction. The crucial dynamical feature we need is a feeble form of specification. All expansions named above generate subshifts with this property. Hence the sets of normal numbers under consideration are $\Pi^0_3$-complete.

18. 12. 2019

M. Mlíchová, Senzitivity v diskrétních dynamických systémech (On sensitivity in discrete dynamical systems). Habilitační přednáška.

11. 12. 2019

P. Blaschke, „Dobývání perihelia; testování teorie gravitace".
J. Bradík, Informace o připravované diplomové práci.

16. 10. 2019

V. Pravec, seminář se bude mimořádně konat v zasedací místnosti na Olbrichově ulici.

9. 10. 2019

L. Rucká a J. Smítal - pracovní seminář.

2. 10. 2019

Seminář se nekoná - Akademický den SU a Vědecká rada SU.

25. 9. 2019

J. Smítal a M. Štefánková, Úvodní seminář.

Seminař se bude konat zpravidla každý sudý týden, v liché týdny se bude ve stejnou dobu (středa 14:00–15:30) a na stejném místě (posluchárna R1) konat seminář prof. Smítala.