Jakob Führer

Many mathematical patterns cannot be avoided. A famous example is the following: if you colour every country on a world map in red, blue, or green, then there will always be two neighbouring countries with the same colour.

In this project, the pattern of interest is the arithmetic progression—a sequence of numbers or points on a line where each step has the same length.

By combining ideas from combinatorics, geometry, and number theory, we study how many colours are needed to avoid such patterns in different algebraic structures and geometric spaces.