Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Algebraic aspects of collapses and bubbles of Calabi-Yau metrics
Some algebraic theories have been occasionally helpful in the study of canonical Kahler metrics e.g. recent technical developments in K-stability. However, much of them are limited to the existence problem in the Einstein case with positive Ricci curvature or its similar variants and do not give much insight into the classical Ricci-flat Kahler (RFK) case for instance. The general aim of this talk is to explain other independent algebraic approaches (algebraic geometry/non-Archimedean geometry/Lie theory) to determine and describe bubbles and collapses of Calabi-Yau metrics. In particular, we have the following topics in mind and will choose some among them:
(1) algebraic construction of (conjectural) bubbling complete affine RFK metrics with Euclidean volume growth, arXiv:2406.14518.
(2) determine collapses of polarized K3 surfaces including limit measures (with Y.Oshima), arXiv:1810.07685, arXiv:2010.00416.
(3) Possible “open K-polystability” notion for the existence problem of complete RFK metrics with small volume growth, arXiv:2009.13876.
(4) Relation with non-archimedean CY metrics and galaxy models (with K.Goto), arXiv:2206.14474 arXiv:2011.12748.
No technicalities in algebraic geometry nor non-archimedean geometry will be assumed.
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