# Colloquium abstracts

**Karl Schwede**

University of Utah

August 26, 2021

**Mixed characteristic birational algebraic geometry**: Recently, Bhargav Bhatt has proved a vanishing theorem for sheaf cohomology on certain non-Noetherian schemes. I will explain how this vanishing theorem is related to various classical vanishing results in characteristic zero and p. I will then discuss how we can use this to prove geometric results in birational algebraic geometry in mixed characteristic. This is joint work with Bhatt, Ma, Patakfalvi, Tucker, Waldron and Witaszek.