Research page of Fabio Pusateri

Research Page of Fabio Pusateri

I am an Associate Professor at University of Toronto. Here is my Curriculum Vitae

My main interests are Analysis of nonlinear PDEs, Dispersive and Wave Equations, Fluid Dynamics, Harmonic Analysis

I support Federico Ardila's axioms:
Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4. Every student deserves to be treated with dignity and respect.

TIDE (Toronto initiative for diversity and equity)

Positions

2022 - present: Associate Professor, University of Toronto
2018 - 2022: Assistant Professor, University of Toronto
2014 - 2018: Assistant Professor, Princeton University
2011 - 2014: Post Doc/Instructor and Simons Fellow, Princeton University
2011 Ph.D. New York University
2006 M. Sc. Università Roma Tre

I had the great honor of being a recipient of the following awards : the Coxeter-James prize (2022), the Antonio Ambrosetti Medal (2021), and the ISAAC award (2019).

I am editor an at Nonlinear Analysis. Submit your work here.

I co-organize the Fields Colloquium in Applied Math

Selected works (accepted/published)

Internal modes and radiation damping for quadratic Klein-Gordon in 3d - with T. Léger, 126 pages. To appear in Memoirs of the Amer. Math. Soc.
On the wave turbulence theory of 2d gravity waves, I: deterministic energy estimates - with A. Ionescu and Y. Deng - Comm. Pure Appl. Math. 78 (2025), no. 2, pp. 211-322
Quadratic Klein-Gordon equations with a potential in one dimension - with P. Germain - Forum Math. Pi 10 (2022), Paper No. e17, 172 pages
Bilinear estimates in the presence of a large potential and a critical NLS in 3d - with A. Soffer - Memoirs of the Amer. Math. Soc. Vol. 299 (2024), 107 pages
Birkhoff normal form and long time existence for periodic gravity water waves - with M. Berti and R. Feola - Comm. Pure Appl. Math. 76 (2023), no. 7, pp. 1416-1494
On the global behavior of weak null quasilinear wave equations - with Y. Deng - Comm. Pure Appl. Math. (2020), vol 73, Issue 5, pp. 1035-1099
Long-time existence for multi-dimensional periodic water waves - with A. Ionescu - Geom. Funct. Anal. (2019), vol 29, Issue 3, pp. 811-870
Global solutions of the gravity-capillary water wave system in three dimensions - with Y. Deng, A. Ionescu and B. Pausader - Acta Mathematica 219 (2017), no. 2, pp. 213-402
Global regularity for 2d water waves with surface tension - with A. Ionescu - Memoirs of the Amer. Math. Soc. (2018), vol 256, no. 1227. v+123 pages
Global solutions for the gravity water waves system in 2d - with A. Ionescu - Inventiones Mathematicae 199 (2015), no. 3, pp. 653-804
A new proof of long range scattering for critical nonlinear Schrödinger equations - with J. Kato - Differential and Integral Equations 24 (2011), no. 9-10, pp. 923-940

All publications (by publication year) - By topic + abstracts click here

(Links to Publications on arXiv - MathSciNet - Scholar)

On the wave turbulence theory of 2d gravity waves, II: propagation of randomness - with A. Ionescu and Y. Deng, 74 pages
Linearized dynamic stability for vortices of Ginzburg-Landau evolutions - with J. Palacios, 62 pages
Long time regularity for 3d gravity waves with vorticity - with D. Ginsberg. To apper in Annals of PDE, 92 pages
Local Energy control in the presence of a zero-energy resonance - with J. Palacios, 48 pages
On the wave turbulence theory of 2d gravity waves, I: deterministic energy estimates (link to arXiv version) - with A. Ionescu and Y. Deng - Comm. Pure Appl. Math. 78 (2025), no. 2, pp. 211-322
Asymptotic stability near the soliton for quartic Klein-Gordon in 1D (link to arXiv version) - with A. Kairzhan. - Pure Appl. Anal. 5 (2023), no. 4, 795-832
On the 1d cubic NLS with a non-generic potential (link to arXiv version) - with G. Chen - Comm. Math. Phys. 405 (2024), no. 2, Paper No. 35, 59 pages
Internal mode-induced growth in 3d nonlinear Klein-Gordon equations (link to arXiv version) - with T. Léger - Rend. Lincei Mat. Appl. Vol. 33, no. 3, pp. 695-727
Internal modes and radiation damping for quadratic Klein-Gordon in 3d - with T. Léger, 126 pages. To appear in Memoirs of the Amer. Math. Soc.
Maximal Speed of Quantum Propagation for the Hartree equation (link to arXiv version) - with J. Arbunich, J. Faupin and I. M. Sigal. - Comm. PDE 48 (2023), no. 4, 542-575
On 1d Klein-Gordon equation with a potential and symmetries (link to arXiv version) - with P. Germain and Z. Zhang. - Arch. Ration. Mech. Anal. 247 (2023), 39 pages
Quadratic Klein-Gordon equations with a potential in one dimension (link to arXiv version) - with P. Germain - Forum Math. Pi 10 (2022), Paper No. e17, 172 pages
Bilinear estimates in the presence of a large potential and a critical NLS in 3d - with A. Soffer - Memoirs of the Amer. Math. Soc. Vol. 299 (2024), 107 pages
Maximal Speed of Quantum Propagation (link to arXiv version) - with J. Arbunich, I. M. Sigal and A. Soffer - Lett. Math. Phys. (2021), vol 111, Article no. 62
Long-time behaviour of time-dependent density functional theory (link to arXiv version) - with I. M. Sigal - Arch. Ration. Mech. Anal. (2021), vol 241, 447-473
The 1d nonlinear Schrödinger equation with a weighted L1 potential (link to arXiv version) - with G. Chen - Analysis & PDE 15 (2022), no. 4, 937-982
Birkhoff normal form and long time existence for periodic gravity water waves - with M. Berti and R. Feola - Comm. Pure Appl. Math. 76 (2023), no. 7, 1416-1494
Birkhoff normal form for gravity water waves (pdf) - with M. Berti and R. Feola - Water Waves (2021), 3, 117-126
On the global behavior of weak null quasilinear wave equations (link to arXiv version) - with Y. Deng - Comm. Pure Appl. Math. (2020), vol 73, Issue 5, pp 1035-1099
Long-time existence for multi-dimensional periodic water waves (link to arXiv version) - with A. Ionescu - Geom. Funct. Anal. (2019), vol 29, Issue 3, pp 811-870
Global regularity for 2d water waves with surface tension (link to arXiv version) - with A. Ionescu - Memoirs of the Amer. Math. Soc. (2018), vol 256, no. 1227. v+123 pages
The nonlinear Schrödinger equation with a potential in dimension 1 (link to arXiv version) - with P. Germain and F. Rousset - Ann. Inst. H. Poincaré C (2018), no. 6, 1477-1530
Global solutions of the gravity-capillary water wave system in three dimensions (link to arXiv version) - with Y. Deng, A. Ionescu and B. Pausader - Acta Mathematica 219 (2017), no. 2, 213-402
Recent advances on the global regularity for water waves (link to arXiv version) - with A. Ionescu - Philos. Trans. Roy. Soc. A (2018), vol 376, issue 2111. 28 pages
On the Global Stability of a Beta-Plane Equation (link to arXiv version) - with K. Widmayer - Analysis & PDE 11 (2018), no. 7, 1587-1624
Almost global existence for cubic nonlinear Schrödinger equations in one space dimension (link to arXiv version) - with J. Murphy - DCDS-A (2017), vol. 37, 2077-2102
Asymptotic stability of solitons for mKdV (link to arXiv version) - with P. Germain and F. Rousset - Advances in Mathematics (2016), vol. 299, 272-330
Global analysis of a model for capillary water waves in two dimensions (link to arXiv version) - with A. Ionescu - Comm. Pure Appl. Math. 69 (2016), no. 11, 2015-2071
Global solutions for the gravity water waves system in 2d (link to arXiv version) - with A. Ionescu - Inventiones Mathematicae 199 (2015), no. 3, 653-804
Decay and scattering for the Chern-Simons-Schrödinger equations (link to arXiv version) - with S.-J. Oh - Int. Math. Res. Notices (2015), no. 24, 13122-13147
On Global Solutions of a Zakharov type System (link to arXiv version) - with T. Beck, P. Sosoe and P. Wong - Nonlinearity 28 (2015), no. 9, 3419-3441
Modified scattering for the Boson Star equation (link to arXiv version) - Comm. Math. Phys. 332 (2014), no. 3, 1203-1234
Nonlinear fractional Schrödinger equations in one dimension (link to arXiv version) - with A. Ionescu - Journal of Functional Analysis 266 (2014), no. 1, 139-176
Scattering for the Zakharov system in 3 dimensions (link to arXiv version) - with Z. Hani and J. Shatah - Comm. Math. Phys. 322 (2013), no. 3, 731-753
Space-time resonances and the null condition for first order systems of wave equations (link to arXiv version) - with J. Shatah - Comm. Pure Appl. Math. 66 (2013), no. 10, 1495-1540
Space-Time Resonances and the null condition for wave equations - Boll. Uni. Mat. Ita. 6 (2013), no.3, 513-529
On the limit as the surface tension and density ratio tend to zero for the two-phase Euler equations (link to arXiv version) - J. Hyperbolic Differ. Equ. 8 (2011), no. 2, 347-373
A new proof of long range scattering for critical nonlinear Schrödinger equations (link to arXiv version) - with J. Kato - Differential and Integral Equations 24 (2011), no. 9-10, 923-940
On the one fluid limit for vortex sheets - arXiv 2009, 20 pages
Analytic Lagrangian tori for the planetary many-body problem (link to arXiv version) - with L. Chierchia - Ergodic Theory and Dynamical Systems 29 (2009), no. 3, 849-873

Please note that .pdf files are usually more up to date than the arXiv versions.

Miscellanea

Global solutions of the gravity-capillary water wave system in 3 dimensions, I: energy estimates
Global solutions of the gravity-capillary water wave system in 3 dimensions, II: dispersive estimates
A note on the asymptotic behavior of 2d gravity water waves (2013) - with A. Ionescu.
Some topics in hyperbolic and dispersive PDE - Ph.D. Thesis (2011)
Analytic KAM Tori for the planetary many body problem - Bachelor's Thesis, 201 pp.
On Kolmogorov's 1954 Theorem on the persistence of quasi-periodic motions

Fellowships and Awards

Coxeter-James prize (2022)

Antonio Ambrosetti Medal (2021)

ISAAC award (2019)

Connaught New Researcher Award (2019-2021)

NSERC Grant RGPIN-2018-06487 (2018-2025)

NSF Grant DMS 1265875 (2013-2017)

Simons Fellowship (2011-2014)

Dean's Dissertation Fellowship (2011)