Pietro Mesquita Piccione
Summary
Mathematician working as a postdoc in complex geometry.
Education
- Ph.D in Mathematics2025Sorbonne Université
- M.S. in Mathematics2022Sorbonne Université
- B.S. in Mathemtics2021Universidade de São Paulo
Work Experience
- Postdoc2025 - 2027University of GothenburgSupervisor: David Witt Nyström
Publications
- A non-Archimedean theory of complex spaces and the cscK problem2024Advances in MathematicsIn 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.
- A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem2025arXivJoint 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.
Presentations
- Demi-Journée des doctorant.e.s de l’équipe TGA 20242024IMJ-PRG, Sorbonne UniversitéParis, France
- Séminaire des Thésards of the IMJ2024IMJ-PRG, Université Paris CitéParis, France
- Any Complex Geometry Seminar2024University of California BerkeleyBerkeley, USA
- Graduate Student Seminar Series2024SLMathBerkeley, USA
- Algebraic Geometry Seminar2024University of GlasgowGlasgow, Scotland
- KASS Seminar2024Chalmers UniversityGothenburg, Sweden
- Geometric Analysis Seminar2024BICMROnline
- Séminaire systèmes dynamiques et géométrie2024Laboratoire Angevin de Recherche en Mathématiques, Université d'AngersAngers, France
- Séminaire de géométrie algébrique de Jussieu2024ENS, salle WParis, France
- Mathematics Seminar2025Department of Mathematics, Aarhus University.Aarhus, Denmark
- Complex Analysis Seminar2025University of BayreuthBayreuth, Germany
- Séminaire Géométries ICJ2025Institut Camille Jordan, Université Claude Bernard Lyon 1Lyon, France
- Séminaire de Géométrie complexe2025Institut de Mathématiques de Toulouse, Université de ToulouseToulouse, France
- Geometry Webinar AmSur/AmSul2025Webinar AmSur/AmSulOnline
- MARGE in Brest: Fibrations and Deformations2025Université de Bretagne OccidentaleBrest, France
- Geometry seminar at MPI Leipzig2025Max Plank Institute for Mathematics in the SciencesLeipzig, Germany
- Complex geometry seminar2025Mathematisches Institut, University of MünsterMünster, Germany
- Workshop on Singular canonical Kähler metrics on compact and non-compact manifolds2025Rényi InstituteBudapest, Hungary
Teaching
- Undergraduate course on Calculus II2018University of São Paulo, Escola PolitécnicaRole: Teaching assistant
- Undergraduate course on Introduction to Analysis course2019Instituto de Matemática e Estatística, Universidade de São PauloRole: Teaching assistant
- Undergraduate course on Differentiable functions and series course2019Instituto de Matemática e Estatística, Universidade de São PauloRole: Teaching assistant
- Undergraduate course on Introduction to Algebraic Topology2020Instituto de Matemática e Estatística, Universidade de São PauloRole: Teaching assistant
- Undergraduate course on Topology and Differentiable Calculus I2023Campus Pierre et Marie Curie, Sorbonne UniversitéRole: Teaching assistant4 weekly hours.
- Undergraduate course on Topology and Differentiable Calculus I2024Campus Pierre et Marie Curie, Sorbonne UniversitéRole: Teaching assistant4 weekly hours.
- Undergraduate course on Functional Analysis2024Campus Pierre et Marie Curie, Sorbonne UniversitéRole: Teaching assistant4 weekly hours.
- Master's course on Introduction to Riemann Surfaces2025Campus Pierre et Marie Curie, Sorbonne UniversitéRole: Teaching assistant6 weekly hours.
- Graduate course on Riemann Surfaces2026Chalmers UniversityRole: Instructor4 weekly hours.
Languages
- PortugueseMother tongue
- ItalianMother tongue
- EnglishFluent
- SpanishFluent
- FrenchFluent
- CatalanIntermediate
- SwedishI hope in the next two years :)