https://www.ams.org/news?news_id=6454Xu’s (single-authored) paper “A minimizing valuation is quasi-monomial” proves a conjecture of Jonsson and Mustata on log canonical thresholds and also a conjecture of Li on normalized volumes. In a series of papers with various coauthors (in particular, the papers “Boundedness of moduli of varieties of general type” with Hacon and McKernan and “Uniqueness of K-polystable degenerations of Fano varieties” with Blum), new powerful methods were introduced, and they established a general framework for moduli of K-stable Fano varieties and give detailed descriptions in many cases. This opens up a completely new area of moduli theory, which earlier was assumed to apply only to general type and Calabi-Yau varieties. This can be viewed as a vast expansion of the minimal model program initiated by Shigefumi Mori·
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