Vincent Guedj

Vincent Guedj is a Professor at Paul Sabatier University (University of Toulouse) and Senior Member of the Institut Universitaire de France (IUF). His affiliations include directorship of the Toulouse Institute of Mathematics (2017-2020), leadership of the European Several Complex Variables Consortium, and editorial roles for prominent journals including Annales de l'Institut Fourier and Publicacions Matemàtiques.

His research centers on complex geometry and geometric analysis, with emphasis on:

• Canonical Hermitian metrics (Kähler-Einstein, plurisigned)
• Degenerate complex Monge-Ampère equations
• Kähler-Ricci flows and parabolic pluripotential theory
• Variational methods in singular geometric settings

This work bridges complex analysis, PDE theory, and differential geometry.

His recent publications (2021-2025) demonstrate strong focus on:

• Regularity theory for Monge-Ampère equations on Hermitian manifolds
• Geometric flows with singularities
• Pluripotential techniques for Kähler-Einstein metrics
• Applications to affine and Hessian geometry

Major scientific awards:

• Clay Senior Scholar (2024)
• Grand Prix Charles Defforey (2024)
• Prix Leconte, Académie des Sciences (2020)
• EMS Monograph Award (2016)

He actively advises doctoral students (9 completed, 1 ongoing) and secures substantial funding, including:

• KRIS project (360k€, Fondation Defforey, 2024-2029)
• PARAPLUI (ANR 140k€, 2021-2025)
• HERMETIC (LabeX CIMI 20k€, 2021-2024)

He directs research at Institut de Mathématiques de Toulouse, coordinating international collaborations and conferences like AMAZER (2021) and KAWA workshops.