I am a postdoctoral researcher at EPFL in the Chair of Partial Differential Equations directed by Prof. Joachim Krieger.
Prior to that I obtained a PhD in December 2020 at the Karlsruhe Institute of Technology (KIT) and the Collaborative Research Center 1173 "Wave Phenomena: analysis and numerics". During 09/2019 - 12/2019 I was a visiting student at EPFL.
Contact: EPFL SB MATH PDE mail: tobias dot schmid at epfl dot ch
Batiment MA
Station 8
CH-1024 Lausanne
Recent News:
Talk at Institute Henri Poincaré Paris, June 2025
Talk at 'CY Days in Nonlinear Analysis', Maison Int. de la Recherche CY Cergy Paris Université, May 2025
Talk at Bielefeld University, Oberseminar Analysis, January 29, 2025
Biharmonic wave maps: local wellposedness in high regularity, Nonlinearity 33 (5), 2270 - 2305, arXiv (with S Herr, T Lamm and R Schnaubelt)
Energy bounds for a fourth-order equation in low dimensions related to wave maps, Proc. Amer. Math. Soc. 151 (01), 225 - 237, arXiv
Global results for a Cauchy problem related to biharmonic wave maps, Pure. Appl. Anal. Vol. 6 (2024), No. 3, 657–691, arXiv
Blow up dynamics for the 3D energy-critical nonlinear Schrödinger equation, arXiv preprint, arXiv (123 pages)
Finite time blow up for the energy critical Zakharov system I: approximate solutions, arXiv preprint, arXiv,
(w. J. Krieger, 149 pages)
Finite time blow up for the energy critical Zakharov system II: exact solutions, arXiv preprint, arXiv,
(with J. Krieger, 169 pages)
Multisoliton solutions and blow up for the L^2-critical Hartree equation, arXiv preprint, arXiv,
(with Jaime Gómez and Yutong Wu)
Verification of spectral assumptions in 6. (Link)
Verification of absence of embbedded eigenvalues in 4. (Link )
Jan 2021 - now: Collaborateur Scientifique (Postdoc) : École Polytechnique Fédérale de Lausanne (EPFL)
Oct 2016 -Dec 2020: PhD: Karlsruhe Institue of Technology (KIT)/ DFG CRC1173 "Wave
Phenomena: Analysis and Numerics"
Talk at Michigan State University, Analysis and PDE Seminar, October 30, 2024
Talk at AMS Fall Western Sectional Meeting 2024, Special Session on Dynamics of Solutions to Wave Equations, UC Riverside, 26 October 2024
ESI Vienna on 21st of May 2024
Bielefeld University, 10th of January 2024
Co-organized conferences/workshops:
workshop 'Young researchers in deterministic and probabalistic dispersive PDE', Bernoulli Center, Lausanne, 07th-11th Oct. 2024. Funded by Bernoulli Center and SwissMAP Network.
Mini-Symposium '(In)Stability, Dispersion and weak turbulence: from fluid flow to Hamiltonian systems', Karlsruhe, 25th- 28th Feb. 2025