Matthew Rosenzweig's Webpage

About me:

My name is Matthew "Matt" Rosenzweig. I am a graduate student in mathematics at the University of Texas at Austin under the supervision of Professor Natasa Pavlovic in my final year. Previously, I completed my undergraduate degree at Harvard University. Here is a copy of my CV.

Email Address: rosenzweig.matthew@math.utexas.edu

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. Mean-Field Convergence of Point Vortices without Regularity, in preparation.
  3. Old and New Perspectives on Effective Equations: A Study of Quantum Many-Body Systems, dissertation (2020).
  4. Global Well-Posedness and Scattering for the Hartree Equation at $L^{2}$-Critical Regularity, preprint (2019).
  5. The Mean-Field Limit of the Lieb-Liniger Model, https://arxiv.org/abs/1912.07585 (2019).
  6. Poisson Commuting Energies for a System of Infinitely Many Bosons, w/ D. Mendelson A.R. Nahmod, N. Pavlovic, and G. Staffilani, https://arxiv.org/abs/1910.06959 , preprint (2019).
  7. A Rigorous Derivation of the Hamiltonian Structure for the Nonlinear Schrodinger Equation, w/ D. Mendelson, A.R. Nahmod, N. Pavlovic, and G. Staffilani, https://arxiv.org/abs/1908.03847, preprint (2019).
  8. Rigorous Justification of the Point Vortex Approximation for Modified Surface Quasi-Geostrophic Equations, https://arxiv.org/abs/1905.07351, preprint (2019).
  9. Global Well-Posedness and Scattering for the Elliptic-Elliptic Davey-Stewartson System at $L^{2}$-Critical Regularity, https://arxiv.org/abs/1808.01955, preprint (2018).

Notes and Expository Material:

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

  1. Convolution inequalities for Boltzmann collision operator - These notes are based on the work by Alonso, Carneiro, and Gamba.
  2. 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.
  3. 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.