Pietro Mesquita Piccione

Pietro Mesquita Piccione

Postdoc in complex geometry

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publications

A non-Archimedean theory of complex spaces and the cscK problem

Published in Advances in Mathematics, 2024

In this paper I construct a space of valuations attached to a compact complex manifold, that generalize the Berkovich analytification of a projective variety over \( \mathbf C \). As an application I get a sufficient algebraic condition for the existence of constant scalar curvature Kähler metrics on a given Kähler class on a Kähler manifold.

Recommended citation: P. Mesquita-Piccione. (2025). "A non-Archimedean theory of complex spaces and the cscK problem." Adv. Math.. 481: Paper No. 110543.
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A transcendental non-Archimedean Calabi–Yau Theorem with applications to the cscK problem

Published in arXiv, 2025

Joint with David Witt Nyström. In it we solve the non-Archimedean Monge-Ampère equation for compact Kähler manifolds, generalizing a result of Boucksom–Favre–Jonsson to the transcendental setting. This allows us to derive a valuative criterion for uniform K-stability for models. As a central application, we prove that this stability condition implies the existence of a unique constant scalar curvature Kähler metric.

Recommended citation: P. Mesquita-Piccione, D, Witt Nyström (2025). "A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem." Preprint, arXiv:2509.09442 [math.AG].
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talks

teaching

Teaching assistant for Calculus II

Undergraduate course, University of São Paulo, Escola Politécnica, 2018

Teaching assistant on a Calculus II course, I was one of two TAs responsible for 800 students at the engendering school of the University of São Paulo.