Speaker: Tran-Trung Nghiem, Université de Montpellier

Time: 09:00-10:00 a.m., April 3, 2024, GMT+8

Venue: online（zoom：861 1625 0516,  Password: 824116）

Abstract: 

On complex symmetric spaces of rank one, Stenzel constructed explicit examples of Calabi-Yau metrics with smooth cross-section asymptotic cone. A new feature in higher rank is that the possible candidates for asymptotic cones generally have singular cross-section.
After an introduction and survey of known results, I will present an existence theorem of Calabi-Yau metrics on symmetric spaces of rank two with asymptotic cone having singular cross-section. This provides new examples of Calabi-Yau manifolds with irregular asymptotic cone besides the only known example of Conlon-Hein, and covers the rank two symmetric spaces left by Biquard-Delcroix. The metrics on the decomposable cases turn out to be asymptotically a product of two Stenzel cones. If time allows, I will also try to explain why some special symmetric spaces of rank two don't have any invariant Calabi-Yau metrics with a given asymptotic cone, using an obstruction on the valuation induced by such metric if exists.

Source: School of Mathematical Sciences, PKU