Singularities in characteristic p and the Riemann–Hilbert correspondence (Robert Cass, CMC)

The Riemann–Hilbert correspondence relates algebra to differential equations on complex algebraic varieties. In characteristic p, there is an analogous correspondence due to Emerton–Kisin and later generalized by Bhatt–Lurie, where the derivative operator is replaced by the p-th power Frobenius operator. In this talk we will explain a relation between the mod p Riemann–Hilbert correspondence and the study of singularities of algebraic varieties in characteristic p. This talk is mostly about commutative algebra, and we will introduce concepts such as local cohomology and perverse sheaves along the way. This is joint work with João Lourenço.