Pietro Mesquita Piccione

Pietro Mesquita Piccione

Postdoc in complex geometry

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Pages

Posts

Future Blog Post

less than 1 minute read

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This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.

Blog Post number 4

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

less than 1 minute read

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Blog Post number 2

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 1

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

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.