Research

I am interested in Hydrodynamic and Wave Turbulence, Dispersive and Kinetic PDEs, Probability and Harmonic Analysis.

Articles:

1. R. Grande, Resonant large deviations principle for the beating NLS equation, preprint (2024)   [arXiv]
2. R. Grande, Z. Hani, Rigorous derivation of damped-driven wave turbulence theory, preprint (2024)   [arXiv]
3. M. Dolce, R. Grande, On the convergence rates of discrete solutions to the Wave Kinetic Equation, Math. Eng. 6 (4), 536-558 (2024)   [arXiv]
4. G. Beck, C.-E. Bréhier, L. Chevillard, R. Grande, W. Ruffenach, Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: applications to fluid turbulence and generation of fractional Gaussian fields, Phys. Rev. Research 6, 033048 (2024)   [arXiv]
5. G.B. Apolinario, G. Beck, L. Chevillard, I. Gallagher, R. Grande, A Linear Stochastic Model of Turbulent Cascades and Fractional Fields, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (2023)   [arXiv]
6. M. Garrido, R. Grande, K. Kurianski, G. Staffilani, Large deviations principle for the cubic NLS equation, Comm. Pure Appl. Math. 76, 4087-4136 (2023)   [arXiv]
7. R. Grande, Continuum limit for discrete NLS with memory effect, to appear in Journal of Nonlinear Modeling and Analysis (2024)   [arXiv]
8. R. Grande, K. M. Kurianski, G. Staffilani, On the nonlinear Dysthe equation, Nonlinear Analysis 207, 112292 (2021)   [arXiv]
9. R. Grande, Space-time fractional nonlinear Schrödinger equation, SIAM J. Math. Anal. 51(5), 4172-4212 (2019)   [arXiv]
10. R. Grande, I. Kovács, K. Kutnar, A. Malnič, L. Martínez, D. Marušič, Equisizable partial sum families, J. Algebr. Comb. 51, 273–296 (2020)
11. M. Conder, R. Grande, On embeddings of circulant graphs, Electronic Journal of Combinatorics 22, P2.28 (2015)

Proceedings:

12. G. Beck, C.-E. Bréhier, L. Chevillard, R. Grande, W. Ruffenach, A linear model of dynamical sea wavenumber spectra, preprint (2025)   [hal]

Teaching and Mentoring

At SISSA:

• Winter 2025: Wave kinetic equations: Global solutions and long-term behavior
• Summer 2024: Master thesis supervisor
  • Student: Riccardo Berforini D'Aquino
  • Project: Large Deviations Principle for the Korteweg-de Vries Equation over long timescales
• Winter 2024: Weak Turbulence and Wave Kinetic Equation

At UMich:

• Summer 2021: REU co-mentor (with Zaher Hani)
  • Students: Yubing Cui and Joshua Messing
  • Project: Wave Kinetic Equation and Kolmogorov-Zakharov Cascade Spectra
• Winter 2021: Math 316 - Differential Equations
• Fall 2020: Math 116 - Calculus II

As a grad student at MIT:

• Spring 2020: Grader for 18.615 - Introduction to Stochastic Processes
• Fall 2019: Grader for 18.085 - Computational Science and Engineering I
• Spring 2019: Grader for 18.615 - Introduction to Stochastic Processes
• Summer 2018: UROP+ mentor
  • Student: Zixuan Xu
  • Project: Almost Conservation Laws for KdV and Cubic NLS
• Spring 2018: TA for 18.03 - Differential Equations
• Fall 2017: TA for 18.02 - Multivariable Calculus
• Fall 2016: Grader for 18.085 - Computational Science and Engineering I
• Summer 2016: UROP+ mentor
  • Student: Eli Sadovnik.
  • Project: A Central Limit Theorem for Fluctuations of Internal DLA with Multiple Sources

Events

Future Perspective on Wave Dynamics

Location: Hotel "Il Cervo" Via Priesnig, 72, 33018 Tarvisio UD

Dates: June 30 - July 4, 2025

The conference explores key challenges in wave dynamics, focusing on quasi-integrability, turbulence, and rogue waves. Set in Tarvisio, Italy, the conference will bring together researchers to discuss recent advances and open questions in these areas.

In order to participate and/or propose a contributed talk, click here.

Organizers: M. Gallone, R. Grande, B. Langella, A. Maspero

CV

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