After successful completion of the course, students are able to observe various Ramsey-type phenomena in different branches of mathematics, and apply connections between combinatorial and dynamical notions in this context.
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size.
More precisely, it is the study of quesions of the following type: given a combinatorial structure (e.g. a graph or a subset of the integers), how large does the structure have to be to guarantee the existence of some substructure (e.g. subgraph, subset) with a given property?
We investigate connections of such questions with various branches of mathematics such as topological dynamics, and applications e.g. to arithmetics, universal algebra, or theoretical computer science.
Each student gives about 2 lectures on selected topics.
Continuous assessment.
Not necessary
Logic or algebra.
