Study of singularities in the minimal model theory in higher dimension

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I reduced the boundedness of minimal log discrepancies to the boundedness of multiplicities or embedding dimensions by using Riemann-Roch theorem, and through the analysis of Artinian rings as hyperplane sections, I recovered this boundedness in dimension 3 and the characterisation of 3-fold Gorenstein terminal singularities. From the point of view of the ascending chain condition, I studied the extension of the ideal-adic semi-continuity of log canonical thresholds due to Kollar and de Fernex, Ein, Mustata, to minimal log discrepancies, and proved this semi-continuity in the setting of purely log terminal singularities by using the theory of motivic integration. I studied also the classification of 3-fold divisorial contractions.