Jan Bohr

I am a postdoctoral researcher at the Mathematical Institute of the University of Bonn. My postdoc advisor is Herbert Koch and I am member of the research group Analysis and Partial Differential Equations.

Previously I was a PhD student at the University of Cambridge under the supervision of Gabriel Paternain and member of the research group of Richard Nickl. My PhD-thesis can be found here. Before this I studied at University of Bonn, University of British Columbia and MLU Halle-Wittenberg.

I am interested in inverse problems and the analysis and geometry at their foundation. The tools I use come from differential geometry, partial differential equations, microlocal analysis and Bayesian non-parametric statistics.

Mathematisches Institut der Universität Bonn Endenicher Allee 60 D-53115 Bonn Office 2.013 Email: surname@math.uni-bonn.de

Teaching

• ▪ Summer 2024: Selected Topics Course on Geometric Inverse Problems
• ▪ Summer 2023: Graduate Seminar on the Calderón Problem

Articles and Preprints

1. Stability of the non-abelian X-ray transform in dimension ≥ 3
   Journal of Geometric Analysis 31 (2021) ▪ arXiv
2. On log-concave approximations of high-dimensional posterior measures and stability properties of non-linear inverse problems (with R. Nickl )
   To appear in Annales de l'Institut Henri Poincaré (Probab. Stat.) ▪ arXiv (2021)
3. The transport Oka-Grauert principle for simple surfaces (with G. P. Paternain )
   Journal de l'École polytechnique 10 (2023) ▪ arXiv
4. A Bernstein-von-Mises theorem for the Calderón problem with piecewise constant conductivities
   Inverse Problems 31 (2023) ▪ arXiv
5. Invariant distributions and the transport twistor space of closed surfaces (with T. Lefeuvre and G. P. Paternain )
   To appear in Journal of the London Mathematical Society ▪ arXiv (2023)
6. Local and global blow-downs of transport twistor space (with F. Monard and G. P. Paternain )
   Preprint: arXiv (2024)

Invited Talks

• On Stability and range for a class of nonlinear X-ray transforms ▪ slides ▪ video
  November 2021 ▪ BIRS workshop: Statistical Aspects of nonlinear Inverse Problems
• The transport Oka-Grauert principle for simple surfaces ▪ slides
  March 2022 ▪ Conference on Rigidity, Hyperbolic Dynamics and Inverse Problems, Roscoff
• The transport Oka-Grauert principle for simple surfaces ▪ slides
  August 2022 ▪ Inverse Problems in Analysis and Geometry, University of Helsinki
• On transport twistor spaces ▪ slides
  November 2022 ▪ Workshop on Geometrical Inverse Problems, Radon Institute Linz
• A BVM theorem for the Calderón problem with pw constant conductivities ▪ slides
  April 2023 ▪ Workshop on Theory for Scalable, Modern Statistical Methods, Bocconi University, Milano
• Looking for structure in the range of some two-dimensional inverse problems ▪ slides
  September 2023 ▪ 11th Applied Inverse Problems Conference, Göttingen
• Local and global blow-downs of transport twistor space ▪ slides
  December 2023 ▪ IAS Workshop on Inverse Problems, Imaging and PDE , Hongkong

Seminar Talks

• The transport Oka-Grauert principle for simple surfaces
  October 2021 ▪ University of Cambridge, Differential Geometry and Topology Seminar
• The transport Oka-Grauert principle for simple surfaces
  November 2021 ▪ Graduate Seminar on Advanced Topics in PDE, University of Bonn
• On transport twistor spaces
  November 2022 ▪ Analysis and Geometry Seminar, Universitaire de Jussieu
• On transport twistor spaces
  March 2023 ▪ Analysis and Geometry Seminar, University of Santa Cruz
• On transport twistor spaces
  March 2023 ▪ Inverse Problems Seminar, University of Washington