The second lecture of the CRN Seminar will take place on Tuesday, March 26, 2024, at 1:15 p.m. in room A.1.3 in building C-19 (and online). Our speaker will be

Prof. Wojciech Samotij (Tel Aviv University)

who will give a lecture

Ramsey properties of random graphs

Abstract:

The well-known theorem of Ramsey implies that every red/blue-colouring of the edges of K₆, the complete graph on six vertices, must contain a monochromatic triangle. Are there graphs that do not contain a K₆ as a subgraph and still have this property? Forty years ago, this innocent question motivated the study of Ramsey and extremal properties of random graphs, an area of research that remains very active to this day. The aim of this talk is to provide a gentle introduction to this area, answering the above question along the way.

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 (and online). 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.