# Behavior of some invariants in characteristic $p$

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Shiji Lyu, Princeton University
Fine Hall 322

In-Person Talk

There are many numerical invariants of a ring in characteristic $p$ measuring its singularity. In this talk, we will discuss two classical ones, Hilbert-Kunz multiplicity and the $F$-signature, and a rather recent one, the $F$-rational signature. We will discuss several properties of these invariants, including semi-continuity and behavior under smooth extensions.