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Award ID contains: 2231783

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  1. ; (, The Journal of Geometric Analysis)
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  2. ; (, Journal of Functional Analysis)
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  3. ; (, Cambridge Journal of Mathematics)
    We construct canonical positive currents and heights on the bound- ary of the ample cone of a K3 surface. These are equivariant for the automorphism group and fit together into a continuous fam- ily, defined over an enlarged boundary of the ample cone. Along the way, we construct preferred representatives for certain height functions and currents on elliptically fibered surfaces. 
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  4. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    We study the collapsing of Calabi–Yau metrics and of Kähler–Ricci flows on fiber spaces where the base is smooth.We identify the collapsed Gromov–Hausdorff limit of the Kähler–Ricci flow when the divisorial part of the discriminant locus has simple normal crossings.In either setting, we also obtain an explicit bound for the real codimension-2 Hausdorff measure of the Cheeger–Colding singular set and identify a sufficient condition from birational geometry to understand the metric behavior of the limiting metric on the base. 
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