Title: Mixed characteristic analogues of Frobenius-split singularities

Abstract: In my talk I will discuss a way to generalise the notion of Frobenius splitting to mixed characteristic. I will also discuss how this circle of ideas can be applied to help us understand singularities in characteristic zero better. This is based on joint work with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, and Joe Waldron.