My primary research interests are in mathematical physics and differential geometry. I investigate integrable systems from a geometric viewpoint, seeking to integrate techniques from complex analysis and differential geometry. Additionally, I am interested in quadratic differentials and their relation to the Stokes phenomenon in the context of the Rabi problem.

Recently, my work has focused on diffeomorphism groups, particularly on the curvature properties of diffeomorphism groups associated with non-orientable manifolds such as the Klein bottle and the projective plane. As a next step, I plan to generalize the theory of curvature from diffeomorphism groups to diffeomorphism groupoids. This generalization has potential applications in fluid dynamics, especially in modeling the flow of multiple non-mixing fluids on manifolds

I have a deep passion for mathematics and love sharing it, whether through crash courses, pub lectures, or dinner conversations. Of academic relevance, I have undertaken the following outreach activities:

• Mars 2025. Poster session and organizer of the winter school "Geometric Analysis", Geilo, Norway.
  • Postertittel: Curvature in the Group of Diffeomorphisms for Non-Orientable Manifolds
• July 2024. Poster session and organizer of the conference "Lie groups, geometry, integrability, hydrodynamics", Nordfjordeid, Norway.
  • Poster title: Curvature in the Group of Diffeomorphisms for Non-Orientable Manifolds
• December 2023. Talk at the program "Order and Randomness in Partial Differential Equations", at Institut Mittag-Leffler, Sweden.
  • Talk title "Stokes graph of a quadratic differential related to a Rabi model"
• August 2023. Main organizer of NNPM 2023: Norwegian National PhD meeting in Mathematics, NTNU Trondheim, Norway.
• Januar 2023. Seminar "The direct monodromy problem and isomonodromic deformations for the Rabi model", at the Department of Mathematics and Systems Analysis, Aalto University, Esbo, Finland.

• Fall 2024: Seminar leader in MAT212
• Spring 2024: Teaching assistant in MAT121
• Fall 2024: Lecturer in MAT101
• Spring 2023: Lecturer and teaching assistant in MAT213
• Fall 2022: Seminar leader in MAT111
• Spring 2022: Seminar leader in MAT213
• Fall 2021: Seminar leader in MAT211
• Spring 2021: Teaching assistant in MAT112
• Fall 2020: Seminar leader in MAT100
• Spring 2020: Seminar leader in MAT112
• Fall 2019: Seminar leader in MAT111
• Spring 2019: Teaching assistant in MAT121
• Fall 2018: Teaching assistant in MAT111

See a complete overview of publications in Cristin.

2025

• Khesin, Boris; Langøen René; Markina, Irina. Curvature of Measure-Preserving Diffeomorphism Groups of Non-Orientable Surfaces. 2025, Nonlinearity, 38, 055017

2024

• Langøen, René; Markina, Irina; Solynin, Alexander. Stokes Graphs of the Rabi Problem with Real Parameters. Journal of Mathematical Sciences 2024 s. 1-58

2022

• Langøen, René. The direct monodromy problem and isomonodromic deformations for the Rabi model. Bergen Open Research Archive 2022