Abstract: In Kähler Geometry, the Yau–Tian–Donaldson Conjecture relates the differential geometry of compact Kähler manifold with an algebro-geometric notion called K-stability. I will start with a brief overview of the topic, and then I will discuss a possible non-Archimedean approach to solve this conjecture, generalizing a result of Chi Li to the transcendental setting.

Biography: Pietro Mesquita-Piccione is a PhD student in Mathematics at the Institut de Mathématiques de Jussieu at Sorbonne Université, in France, working under the supervision of Sébastien Boucksom and Tat Dat Tô. He completed a Master's degree at the same institution and a Bachelor's degree at the University of São Paulo, in Brazil. His research is focused on Complex Geometry, with an emphasis on the relation between non-Archimedean geometry and canonical Kähler metrics.

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