Singularities in mixed characteristic via the Riemann-Hilbert correspondence

In my talk, I will start by reviewing how various properties of characteristic zero singularities can be understood topologically by ways of the Riemann-Hilbert correspondence. After that, I will explain how similar ideas can be applied in the study of mixed characteristic singularities. This is based on a joint work with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, and Joe Waldron.