Valentino Tosatti

About

Valentino Tosatti is a Professor of Mathematics and Vice Dean for Faculty Affairs at the Courant Institute, School of Mathematics, Computing, and Data Science at New York University. His research areas encompass complex and differential geometry, geometric analysis, and partial differential equations, with connections to algebraic geometry and dynamical systems. His work includes specific topics such as Kähler geometry, Calabi-Yau manifolds, almost-complex, symplectic, and Hermitian geometry, geometric flows, complex Monge-Ampère equations, transcendental methods in algebraic geometry, and holomorphic dynamics. Tosatti has contributed extensively to the understanding of Calabi-Yau metrics, Kähler-Ricci flows, and degenerations of complex manifolds, among other areas, and has a significant publication record in leading mathematical journals. His expertise combines deep theoretical insights with a focus on the geometric structures underlying complex manifolds, making him a prominent figure in his field.

Research topics

• Mathematics
• Mathematical analysis
• Computer Science
• Pure mathematics
• Physics
• Statistics
• Geometry

Selected publications

• Smooth asymptotics for collapsing Calabi–Yau metrics

  Communications on Pure and Applied Mathematics · 2024-10-09 · 4 citations

  articleOpen accessSenior authorCorresponding

  Abstract We prove that Calabi–Yau metrics on compact Calabi–Yau manifolds whose Kähler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. To this end, we prove an asymptotic expansion of these metrics in terms of powers of the fiber diameter, with ‐order remainders that satisfy uniform ‐estimates with respect to a collapsing family of background metrics. The constants in these estimates are uniform not only in the sense that…

  PublisherOA PDFDOI

• Gaps in the Support of Canonical Currents on Projective K3 Surfaces

  Journal of Geometric Analysis · 2024-01-19 · 2 citations

  articleSenior authorCorresponding
  PublisherDOI

• Special Kähler geometry and holomorphic Lagrangian fibrations

  Comptes Rendus Mathématique · 2024-06-06 · 1 citations

  articleOpen accessSenior authorCorresponding

  Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. The splitting is nontrivial when the base is not half-dimensional projective space. Combining this with results of Voisin, Hwang and Bakker–Schnell, we dedu…

  PublisherOA PDFDOI

• Immortal solutions of the Kähler-Ricci flow

  arXiv (Cornell University) · 2024-05-07 · 1 citations

  preprintOpen access1st authorCorresponding

  We survey some recent developments on solutions of the Kähler-Ricci flow on compact Kähler manifolds which exist for all positive times.

  PublisherOA PDFDOI

• Nonlinearizable embeddings of elliptic curves in rational surfaces

  arXiv (Cornell University) · 2026-05-05

  preprintOpen accessSenior author

  We show that for any smooth cubic in $\mathbb{P}^2$, there exists a dense $G_δ$ set of configurations of 9 distinct points such that blowing up $\mathbb{P}^2$ at these 9 points, the strict transform of the cubic is not linearizable and has nontorsion normal bundle. This answers a problem raised by Ogus in 1975.

  PublisherDOI

Recent grants

• Geometric Partial Differential Equations and Complex Geometry

  NSF · $151k · 2019–2022

• Geometry and Analysis on Calabi-Yau and Hermitian Manifolds

  NSF · $191k · 2013–2016

• Geometric Partial Differential Equations and Complex Geometry

  NSF · $167k · 2022–2024

Frequent coauthors

• Ben Weinkove

  28 shared

• Yuguang Zhang

  27 shared

• Simion Filip

  University of Chicago

  16 shared

• Mark Gross

  12 shared

• Yang Li

  Massachusetts Institute of Technology

  10 shared

• J. M. Landsberg

  Texas A&M University

  9 shared

• Edward Frenkel

  Texas A&M University

  9 shared

• J.G. Morse

  University of California, Berkeley

  9 shared

Similar researchers at New York University

• Jiawei Zhangh-76
• Foster Provosth-60
• Panagiotis Ipeirotish-50