Abstract: In this talk, I will give a counterexample to the PIA (precise inversion of adjunction) conjecture for MLD's (minimal log discrepancy). The usual inversion of adjunction is a type of claim "the information of the singularity of a pair (X,D) can be recovered from the information of the singularity of D". The precise version (PIA conjecture) states that this is correct at the level of MLD (minimal log discrepancy), the invariant of the singularity. The PIA conjecture is known to be true in dimension 3. In this talk, I will give a counterexample in dimension 5. This talk is based on joint work with Kohsuke Shibata.