The Hilbert-Kunz multiplicity and the Frobenius Betti numbers are numerical invariants that can be attached to any local ring of prime characteristic. Other than having interesting properties on their own, they are particularly useful because they measure the singularities of the ring. For instance, Watanabe and Yoshida showed that, under mild assumptions, the Hilbert-Kunz multiplicity is one if and only if the ring is regular. Aberbach and Li proved that these facts are also equivalent to the vanishing of the higher Frobenius Betti numbers. In this talk, we will discuss how to define these invariants for rings that are not necessarily local. We will also discuss how these global invariants relate to the local ones, and how they still measure the singularities of the ring. This is based on joint work with Thomas Polstra and Yongwei Yao. Speaker(s): Alessandro De Stefani (KTH Royal Institute of Technology, Sweden)