Colloquium on Number Theory

Please register your attendance so we can order enough fika.

Programme

Short presentations:

Reza Mohammadpour: From Digit Frequencies to Multifractal Analysis

Abstract: Digit frequency results in number theory, such as the distribution of digits in expansions of real numbers, reveal fascinating patterns with deep mathematical implications. In this talk, I will discuss how these classical results can be extended and reinterpreted through the lens of dynamical systems and ergodic theory. Specifically, I will present connections between digit frequency and multifractal formalism, which provides a framework for understanding the interplay between dynamics, geometry, and statistical properties.

Kirsti Biggs: Diophantine Problems in Fractal Sets

Abstract: Sets of integers with digital restrictions in a given base have a fractal structure which can be viewed as a p-adic analogue of a real Cantor set. In this talk, I will discuss ways in which we can count digitally restricted solutions to various Diophantine problems involving sums of powers, such as Waring's problem and Vinogradov's mean value theorem. Part of this is based on joint work with Julia Brandes.

Arne Beurling's Geheimschreiber

Kirsti gives a short introduction to Beurling's Geheimschreiber. After that, there will be the option to view it.

FIKA

Time for discussing new and old problems in number theory with the specialists in a relaxed atmosphere.