The first lecture of the CRN Seminar will take place on Thursday, October 19, 2023, at 11:15 a.m. in room A.1.14 in building C-19. Our speaker will be

Prof. Tomasz Downarowicz

who will give a lecture

Topological normality preservation by addition.

Abstract:

In this lecture, inaugural for the CRN seminar, I will present something perhaps interesting, very natural and — above all — easy to follow, namely, an answer to the question given below.

A symbolic sequence x over a finite alphabet A = {0, 1, 2, …, r – 1} is called topologically normal if it is transitive in the full shift over A (that is, every finite block of symbols occurs in x). In the shift space we introduce coordinatewise addition modulo r.

Question: What sequences y over A have the property that x + y is topologically normal for every topologically normal sequence x?

The answer is surprising, because it involves a new class of sequences that presumably none of us has ever heard about before.

More information here.