Jonas Lührmann

Mathematisches Institut
Universität zu Köln
Weyertal 86-90
50931 Köln

Office: 0.04

Email: jonas.luehrmann (at) uni-koeln.de

I am a Professor at the Department of Mathematics at the University of Cologne. Previously, I was an Associate Professor in the Department of Mathematics at Texas A&M University, and a J.J. Sylvester Assistant Professor in the Department of Mathematics at Johns Hopkins University. I received my Ph.D. in mathematics from ETH Zurich.

My research is in partial differential equations and mathematical physics. I am particularly interested in the long-time dynamics of nonlinear dispersive and hyperbolic PDEs.

Curriculum Vitae

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Publications

• On the Gross-Pitaevskii evolution linearized around the degree-one vortex
  J. Lührmann, W. Schlag, S. Shahshahani
  Preprint arXiv:2503.07345, 68 pp.
• Asymptotic stability of the sine-Gordon kink
  G. Chen, J. Lührmann
  Preprint arXiv:2411.07004, 181 pp.
• Asymptotic stability of solitary waves for the 1D cubic Schrödinger equation under even perturbations
  Y. Li, J. Lührmann
  Preprint arXiv:2408.15427, 91 pp.
• On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation
  J. Lührmann, W. Schlag
  Comm. Amer. Math. Soc. 4 (2024), 230–356.
• Stability of the catenoid for the hyperbolic vanishing mean curvature equation outside symmetry
  J. Lührmann, S.-J. Oh, S. Shahshahani
  Invent. Math. 240 (2025), no. 3, 903–1044
• Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry
  Y. Li, J. Lührmann
  J. Differential Equations 344 (2023), 172–202.
• The wave maps equation and Brownian paths
  B. Bringmann, J. Lührmann, G. Staffilani
  Comm. Math. Phys. 405 (2024), no. 3, Paper No. 60, 115 pp.
• Asymptotic stability of the sine-Gordon kink under odd perturbations
  J. Lührmann, W. Schlag
  Duke Math. J. 172 (2023), no. 14, 2715–2820.
• On modified scattering for 1D quadratic Klein-Gordon equations with non-generic potentials
  H. Lindblad, J. Lührmann, W. Schlag, A. Soffer
  Int. Math. Res. Not. 2023 (2022), no. 6, 5118–5208.
• Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation
  J. Krieger, J. Lührmann, G. Staffilani
  Arch. Ration. Mech. Anal. 247 (2023), no. 4, 109 pp.
• Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities
  H. Lindblad, J. Lührmann, A. Soffer
  Arch. Ration. Mech. Anal. 241 (2021), no. 3, 1459–1527.
• Asymptotic stability of harmonic maps on ℍ² under the Schrödinger maps evolution
  A. Lawrie, J. Lührmann, S.-J. Oh, S. Shahshahani
  Comm. Pure Appl. Math. 76 (2023), no. 3, 453–584.
• Decay and asymptotics for the 1D KG equation with variable coefficient cubic nonlinearities
  H. Lindblad, J. Lührmann, A. Soffer
  SIAM J. Math. Anal. 52 (2020), no. 6, 6379–6411.
• Local smoothing estimates for Schrödinger equations on hyperbolic space
  A. Lawrie, J. Lührmann, S.-J. Oh, S. Shahshahani
  Mem. Amer. Math. Soc. 291 (2023), no. 1447, v+165 pp.
• Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation
  B. Dodson, J. Lührmann, D. Mendelson
  Adv. Math. 347 (2019), 619–676.
• Almost sure scattering for the 4D energy-critical defocusing NLW equation with radial data
  B. Dodson, J. Lührmann, D. Mendelson
  Amer. J. Math. 142 (2020), no. 2, 475–504.
• Concentration Compactness for Critical Radial Wave Maps
  E. Chiodaroli, J. Krieger, J. Lührmann
  Annals of PDE 4 (2018), no. 1, Art. 8, 148 pp.
  
• Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation
  J. Krieger, J. Lührmann
  Annals of PDE 1 (2015), no. 1, Art. 5, 208 pp.
  
• On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on ℝ³
  J. Lührmann, D. Mendelson
  New York J. Math. 22 (2016), 209–227
• Random data Cauchy theory for nonlinear wave equations of power-type on ℝ³
  J. Lührmann, D. Mendelson
  Comm. Partial Differential Equations 39 (2014), no. 12, 2262–2283
• Mean-field quantum dynamics with magnetic fields
  J. Lührmann
  J. Math. Phys. 53 (2012), no. 2, 19 pp.

Past Conferences and Workshops

• Spring School on Soliton Dynamics
  Texas A&M, March 14-16, 2024
• TexAMP 2024 (Texas Analysis and Mathematical Physics Symposium)
  Texas A&M, February 9-11, 2024
• Trends in Soliton Dynamics and Singularity Formation for Nonlinear Dispersive PDEs
  Texas A&M, October 21-23, 2022

Teaching

• WS 25/26: Introduction to Nonlinear Wave Equations
• WS 25/26: Seminar "Mathematical Quantum Mechanics and Schrödinger Operators"

• Spring 2024: Math 410 Advanced Calculus II
• Spring 2024: Math 308 Differential Equations
• Spring 2023: Math 612 Partial Differential Equations
• Spring 2023: Math 308 Differential Equations
• Fall 2022: Math 611 Introduction to Ordinary and Partial Differential Equations
• Spring 2022: Math 308 Differential Equations
• Spring 2021: Math 410 Advanced Calculus II
• Spring 2021: Math 689 Special Topics Course on Nonlinear Waves and Dispersive Equations
• Spring 2020: Math 410 Advanced Calculus II
• Fall 2019: Math 412 Theory of Partial Differential Equations

• Spring 2019: Math 302 Differential Equations with Applications
• Fall 2018: Math 632 Partial Differential Equations II
• Spring 2018: Math 417 Partial Differential Equations
• Fall 2017: Math 302 Differential Equations with Applications
• Spring 2017: Math 405 Analysis I
• Fall 2016: Math 106 Calculus I (Biology and Social Sciences)