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Nonlinear Analysis

Geometry and analysis of degenerating Calabi-Yau manifolds

Ruobing Zhang, State University of New York at Stony Brook

Location:  Hill 705
Date & time: Tuesday, 04 February 2020 at 1:40PM - 2:50PM

Abstract: This talk concerns a naturally occurring family of Calabi-Yau manifolds with degenerating complex structures. Along an algebraically degenerating family, the underlying Calabi-Yau metrics may collapse in the Gromov-Hausdorff sense, which leads to both geometric and analytic difficulties in understanding the dengeration. We will accurately characterize the degeneration from the metric geometric point of view. Correspondingly, we will also discuss the singularity formation for the corresponding elliptic equations with a focus on the effective estimates and bubble classification. A primary tool in analyzing their behavior is the recently developed regularity theory and multi-scale singularity analysis in the collapsed setting.

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