The study of compatible ideals has been an important part of commutative algebra in positive characteristic in the last decades. In this talk, I will survey some of their properties and explain how they are used. I will also give some key examples like the splitting prime, the test ideal, and the conductor ideal.

The talk will be virtual, but we will have a watch party in our usual room. If you would like the zoom info to attend virtually instead, email an organizer or join our mailing list.