Hilbert-Kunz density function and its applications

Abstract: In this talk, we recall the notion of the Hilbert-Kunz density function for graded rings. This function was introduced to understand the Hilbert-Kunz multiplicity which is a difficult characteristic $p$ invariant to compute and to make speculation about its properties. It turns out the HK density function is also related to another characteristic $p$-invariant namely $F$-threshold. Here we describe its properties and give its applications to HK multiplicity, $F$-thershold, and to a conjecture of Watanabe-Yoshida. The talk is partly based on joint work with K.I. Watanabe.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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