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Workgroup Functional Analysis

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.041

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe


natascha.katz@kit.edu


Office hours:
9:00 - 11:00

Tel.: +49 721 608 43727

Fax.: +49 721 608 67650

Fabian Hornung

Office hour for students:
Room: 2-048 Kollegiengebäude Mathematik (20.30)
Email: fabian.hornung@kit.edu

Karlsruher Institut für Technologie
Fakultät für Mathematik
Institut für Analysis
Englerstraße 2
76131 Karlsruhe





Current List of Courses
Semester Titel Typ
Summer Semester 2018 Seminar
Winter Semester 2017/18 Proseminar
Summer Semester 2017 Seminar
Winter Semester 2016/17 Lecture
Summer Semester 2016 Seminar


Research interests

  • Analysis of stochastic partial differential equations
  • Numerical analysis of highdimensional stochastic and deterministic partial differential equations

Publications

  • Hornung. The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates, Journal of Evolution Equations, 2018 Link
  • Brzezniak, Hornung, Weis. Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space, Probability Theory and Related Fields, online first, 2018. Link

Preprints

  • Brzezniak, Hornung, Manna. Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise, submitted, 2018. Link
  • Brzezniak, Hornung, Weis. Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds, preprint, 2018. Link
  • Grohs, Hornung, Jentzen, von Wurstemberger. A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations, preprint, 2018. Link

Dissertation

Hornung: Global solutions of the nonlinear Schrödinger equation with multiplicative noise. Karlsruhe Institute of Technology. 2018. DOI: 10.5445/IR/1000083044

Talks

  • November 2015: Global wellposedness of a stocahstic nonlinear Schrödinger equation, Research seminar Functional Analysis, Karlsruhe.
  • April 2016: The stochastic NLS on 3d compact manifolds, First annual meeting of the CRC 1173, Rastatt.
  • December 2016: The stochastic Strichartz inequality and applications to the NLS with multiplicative noise, Research seminar Functional Analysis, Karlsruhe.
  • January 2017: An introduction to stochastic PDEs, iRTG Seminar, Karlsruhe.
  • June 2017: Global solutions for the stochastic NLS, Bielefeld Stochastic Afternoon, Bielefeld.
  • July 2017: Global solutions for the stochastic NLS, TULKKA, Ulm.
  • November 2017: On uniqueness of solutions to the NLS, Workshop of the Research Training Groups Karlsruhe-Stuttgart-Tübingen, Karlsruhe.
  • July 2018: Pathwise uniqueness for the stochastic nonlinear Schrödinger equation on 3d compact manifolds, Workshop Harmonic Analysis for stochastic PDE, Delft.
  • July 2018: Stochastic Strichartz estimates and the NLS with multiplicative noise, Minisymposium Stochastic nonlinear wave and Schrödinger equations and applications, Conference on the mathematics of wave phenomena, Karlsruhe.
  • Januar 2019: Neural network approximation for Kolmogorov PDEs, Research seminar Functional Analysis & CRC Wave phenomena, Karlsruhe.