About me

I am an Assistant Professor (RTD-A) at SISSA. Previously, I was a Postdoctoral Researcher at École Normale Supérieure working with Isabelle Gallagher and Laure Saint-Raymond. During 2020-21, I was a Postdoctoral Assistant Professor at the University of Michigan – Ann Arbor working with Zaher Hani. I obtained my PhD from MIT in 2020, under the supervision of Gigliola Staffilani. More about me can be found in my CV. Address: Office A-727, Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy Email: rgrandei [at] sissa [dot] it

Research

I am interested in Hydrodynamic and Wave Turbulence, Dispersive and Kinetic PDEs, Probability and Harmonic Analysis.
Here are some of my publications:

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

Teaching and Mentoring

At SISSA:

• 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

Resources: Students interested in Calculus, Differential Equations or Probability should check out these Mathlets. Students in advanced courses (Functional Analysis, Distribution Theory, Microlocal Analysis, etc.) might be interested in these brief notes about various such topics. Students who are interested in research experience may want to read about UROP and the REU program.

CV

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