# Abstract Lukas Brantner

Speaker: Lukas Brantner (Oxford)

Title: Lie algebras, deformations, and Galois theory in characteristic p.

Abstract: We introduce a derived version of Lie algebras in characteric p and describe two recent applications: first, we use them to classify infinitesimal deformations, generalising the Lurie-Pridham theorem in characteristic zero; second, we prove a Galois correspondence for purely inseparable field extension, extending work of Jacobson at height one. This talk is based on joint works with Mathew and Waldron.