1st talk:
We will give a gentle introduction to K-theory and discuss its relevance in geometric topology and elsewhere.

2nd talk:
We explain how K-theory is related to arithmetic cohomology theories (through topological periodic homology) and how this new found and surpising relation leads to advances in both areas. This relation is the foundational result for Project A4 in the CRC. It can for example be used to calculate K-theory, but it also lead to the newly developed prismatic cohmology theory (of Bhatt and Scholze).