**Haydar Göral, **İzmir Institute of Technology . **Date**: 26th of April, 2024, Friday, **Time**: 13.00 – 14.00. **Place**: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Class B255

**Abstract**: In this talk, we first define ultrafilters on a non-empty set. Then, we see that there is a natural topology on the set of ultrafilters on the positive integers, and in fact this is the Stone-Cech compactification of the positive integers. Moreover, this compact space has an associative binary operation extending the addition of the positive integers. Finally, we will show how this topological semigroup is crucial for proving Ramsey theoretical results from combinatorics.