Matthew Rosenzweig's Webpage

About me:

My name is Matthew "Matt" Rosenzweig. I am a CLE Moore Instructor at MIT and postdoctoral associate of the Simons Collaboration on Wave Turbulence. I defended my dissertation at the University of Texas at Austin in April 2020, under the supervision of Professor Natasa Pavlovic. Previously, I completed my undergraduate degree at Harvard University. Here is a copy of my CV.

Email Address:

Research Interests:

My current research interests are in nonlinear partial differential equations and mathematical physics. More specifically, I have been recently interested in the mathematics of nonlinear dispersive and fluid equations and their derivation from underlying physical problems, such as water waves and quantum many-body systems. More on my mathematical interests can be learned from my research statement.

Papers and Preprints:

  1. Full Justification of the Davey-Stewartson System from 3D Finite-Depth Gravity Water Waves, in preparation.

  2. From Quantum Many-Body Systems to Ideal Fluids, in preparation.

  3. A Rigorous Justification of the Stochastic Point Vortex Model with Multiplicative Noise, in preparation.

  4. Global Solutions to Aggregation Equations and Other Flows with Random Diffusion, w/ G. Staffilani, in preparation.

  5. Global-in-time Mean-Field Convergence for Singular Riesz-type Diffusive Flows, w/ S. Serfaty,, 41 pgs., preprint (2021).

  6. Mean-Field Limits of Riesz-Type Singular Flows with Possible Multiplicative Transport Noise, w/ Q.H. Nguyen and S. Serfaty,, 40 pgs., preprint (2021).

  7. On the Rigorous Derivation of the Incompressible Euler Equation from Newton's Second Law,, 20 pgs., preprint (2021).

  8. Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory,, 25 pgs., preprint (2021).

  9. The Mean-Field Limit of Stochastic Point Vortex Systems with Multiplicative Noise,, 34 pgs., preprint (2020).

  10. Mean-Field Convergence of Systems of Particles with Coulomb Interactions in Higher Dimensions without Regularity,, 32 pgs., preprint (2020).

  11. Mean-Field Convergence of Point Vortices without Regularity, , 47 pgs., preprint (2020).

  12. Old and New Perspectives on Effective Equations: A Study of Quantum Many-Body Systems, dissertation, 398 pgs., (2020).

  13. Global Well-Posedness and Scattering for the Hartree Equation at $L^{2}$-Critical Regularity, preprint, 137 pgs., (2019).

  14. The Mean-Field Limit of the Lieb-Liniger Model,, preprint, 32 pgs., (2019).

  15. Poisson Commuting Energies for a System of Infinitely Many Bosons, w/ D. Mendelson A.R. Nahmod, N. Pavlovic, and G. Staffilani, , 97 pgs., preprint (2019).

  16. A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrodinger Equation, w/ D. Mendelson, A.R. Nahmod, N. Pavlovic, and G. Staffilani,, 81 pgs., preprint (2019).

  17. Rigorous Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations,, 35 pgs., preprint (2019).

  18. Global Well-Posedness and Scattering for the Elliptic-Elliptic Davey-Stewartson System at $L^{2}$-Critical Regularity,, 129 pgs., preprint (2018).

Notes and Expository Material:

Caveat Emptor: the material below is likely riddled with typos.

  1. Beyond Gronwall for gradient flows - A short note showing that in some cases (e.g. Coulomb gradient flow on $\mathbb{R}^d$), one can prove mean-field convergence for noiseless systems of particles with a convergence rate having time factor $O(t^{\delta})$, for some $\delta>0$. While well-known that noise improves the growth in time of the rate (possibly making the rate uniform), it doesn't seem to have been previously observed you can go beyond the Gronwall $e^{Ct}$ growth without noise.

  2. Pickl's method for $H^1$ data - A note showing how to use dispersion of the limiting equation to reduce the regularity assumptions in Pickl's derivation of the 3D Gross-Pitaevskii equation.

  3. Convolution inequalities for Boltzmann collision operator - These notes are based on the work by Alonso, Carneiro, and Gamba.

  4. Critical conditional global well-posedness and scattering for cubic NLS in $\mathbb{R}^{3}$ - These notes are based on the work by Kenig and Merle.

  5. Introduction to Fourier analysis on the torus -- These notes give an introduction to Fourier analysis on the torus $\mathbb{T}^{d}$. The notes include a treatment of Kolmogorov's construction of an $L^{1}(\mathbb{T})$ function whose Dirichlet means diverge pointwise almost everywhere.