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.

Biography: After undergraduate and master studies in Paris at Sorbonne Université and the ENS, I am currently carrying out a PhD thesis under the supervision of Thibaut Delcroix at the Université de Montpellier.

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