Abstract: Non-Archimedean geometry can be viewed as a degeneration of complex geometry. In recent years, it has found applications in the existence problem for canonical metrics via K-stability, particularly for Fano varieties. On the other hand, while the existence of canonical metrics on smooth projective Calabi-Yau varieties is classical, much less is understood in the affine setting. 

In this talk, we discuss some recent progress on the existence problem for canonical metrics on affine Calabi-Yau varieties, focusing on a non-Archimedean perspective. In particular, we present a solution to a corresponding non-Archimedean existence problem in certain cases using a kind of non-Archimedean spaces called Berkovich spaces. We also explain how this non-Archimedean solution relates to the original complex analytic problem.

Brief biography: Ying Wang is currently a Ph.D. student at University of Michigan, under the guidance of Professor Mattias Jonsson. Her research focuses on non-archimedean geometry, algebraic geometry, and complex geometry.

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