About

I am a postdoctoral researcher in the group of Sebastian Herr at the Department of Mathematics at the University of Bielefeld.
I am a member of Project A1: Nonlinear interactions of rough waves of the CRC 1283 Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications in Bielefeld.

Before coming to Bielefeld, I was a postdoctoral researcher in Project A5: Qualitative behavior of nonlinear Maxwell equations of the CRC 1173 Wave Phenomena: Analysis and Numerics at the Karlsruhe Institute of Technology, where I also obtained my PhD under the supervision of Roland Schnaubelt.

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Research interests

My research interests lie in the field of nonlinear dispersive and hyperbolic partial differential equations. I am interested in their low regularity well-posedness theory, qualitative properties, and long-time behavior. I also study the influence of randomness on the behavior of dispersive PDEs, investigating both problems with randomized data and problems with noise.

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Teaching

Most of my teaching activities at Bielefeld University can be found on my eKVV page.

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Preprints

• Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations
  M. Spitz, D. Zhang, and Z. Zhao
  arXiv:2505.05421, 14 pages, 2025.

  ArXiv

• The energy-critical stochastic Zakharov system
  S. Herr, M. Röckner, M. Spitz, and D. Zhang
  arXiv:2410.05034, 56 pages, 2024.

  ArXiv

• Modified scattering for the three dimensional Maxwell-Dirac system
  S. Herr, M. Ifrim, and M. Spitz
  arXiv:2406.02460, 64 pages, 2024.

  ArXiv

Publications

• The three-dimensional stochastic Zakharov system
  S. Herr, M. Röckner, M. Spitz, and D. Zhang
  The Annals of Probability 53:3 (2025), 848--905.

  ArXiv

  Journal

• Local well-posedness of a system describing laser-plasma interactions
  S. Herr, I. Kato, S. Kinoshita, and M. Spitz
  Vietnam Journal of Mathematics. Special issue dedicated to Carlos Kenig on the occasion of his 70th birthday 51:4 (2023), 759--770.

  ArXiv

  Journal

• Almost sure local wellposedness and scattering for the energy-critical cubic nonlinear Schrödinger equation with supercritical data
  M. Spitz
  Nonlinear Analysis 229 (2023), Paper No. 113204.

  ArXiv

  Journal

• Local wellposedness of quasilinear Maxwell equations with conservative interface conditions
  R. Schnaubelt and M. Spitz
  Communications in Mathematical Sciences 20:8 (2022), 2265--2313.

  ArXiv

  Journal

• On the almost sure scattering for the energy-critical cubic wave equation with supercritical data
  M. Spitz
  Communications on Pure and Applied Analysis 21:12 (2022), 4041--4070.

  ArXiv

  Journal

• Randomized final-state problem for the Zakharov system in dimension three
  M. Spitz
  Communications in Partial Differential Equations 47:2 (2022), 346--377.

  ArXiv

  Journal

• Regularity theory for nonautonomous Maxwell equations with perfectly conducting boundary conditions
  M. Spitz
  Journal of Mathematical Analysis and Applications 506:1 (2022), Paper No. 125646.

  ArXiv

  Journal

• Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions
  R. Schnaubelt and M. Spitz
  Evolution Equations and Control Theory 10:1 (2021), 155--198.

  ArXiv

  Journal

• Local wellposedness of nonlinear Maxwell equations with perfectly conducting boundary conditions
  M. Spitz
  Journal of Differential Equations 266:8 (2019), 5012--5063.

  ArXiv

  Journal

PhD Thesis

• Local wellposedness of nonlinear Maxwell equations
  M. Spitz
  Karlsruhe Institute of Technology, 2017.

  DOI

Recent and upcoming talks

May 2025	Conference Theoretical and numerical analysis of multi-scale equations, Lyon
April 2025	Mini-course: Modified scattering for the three dimensional Maxwell-Dirac system, Shanghai Jiao Tong University
February 2025	Conference on Mathematics of Wave Phenomena 2025, Karlsruhe Minisymposium Recent Methods in Nonlinear Dispersive Waves
October 2024	Conference Young researchers in deterministic and probabilistic dispersive equations, Lausanne
September 2024	Analysis seminar, Institut Denis Poisson, Tours
June 2024	Conference Harmonic and Stochastic Analysis of Dispersive PDEs, Bielefeld
March 2024	Stochastic Analysis Seminar, Shanghai Jiao Tong University, Shanghai