The minimal log discrepancy is an invariant of singularities defined in birational geometry, and it is related to the conjecture of termination of flips. In this talk, we will discuss the minimal log discrepancies of quotient singularities. I will show that the PIA (precise inversion of adjunction) conjecture holds for quotient singularities. The main tool of this talk involves the theory of the arc space of a quotient singularity established by Denef and Loeser. This is joint work with Kohsuke Shibata.

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