Hans Munthe-Kaas
Director
Professor · University of Bergen
About
Hans Munthe-Kaas is an internationally recognized pioneer in geometric numerical integration and Lie group methods. His foundational work on Runge-Kutta methods for manifolds and Lie group integrators has shaped how computational scientists approach structure-preserving numerical algorithms across physics, engineering, and applied mathematics.
As Co-Director of the Lie–Størmer Center, Hans provides strategic leadership connecting Norwegian mathematics to the global research community. His vision for the Center emphasizes the deep interplay between algebraic structures and computational methods — building on the legacy of Norwegian mathematicians Sophus Lie and Carl Størmer, whose work continues to influence modern differential geometry and dynamical systems.
Hans has made seminal contributions to the theory of B-series and combinatorial Hopf algebras in numerical analysis, revealing elegant algebraic structures underlying classical integration methods. His current research explores connections between rough path theory, regularity structures, and geometric numerical methods, advancing the mathematical foundations that enable reliable simulation of complex physical systems.
Selected Publications
- Lie Admissible Triple Algebras: The Connection Algebra of Symmetric Spaces, with Hans Z. Munthe-Kaas, Jonatan Stava, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) (2024).
- The Universal Equivariance Properties of Exotic Aromatic B-series, with Adrien Laurent, Hans Z. Munthe-Kaas, Foundations of Computational Mathematics (2024).
- The Aromatic Bicomplex for the Description of Divergence-Free Aromatic Forms and Volume-Preserving Integrators, with Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas, Olivier Verdier, Forum of Mathematics, Sigma (2023).
- Planarly Branched Rough Paths and Rough Differential Equations on Homogeneous Spaces, with Charles Curry, Kurusch Ebrahimi-Fard, Dominique Manchon, Hans Z. Munthe-Kaas, Journal of Differential Equations (2020).
- Invariant Connections, Lie Algebra Actions, and Foundations of Numerical Integration on Manifolds, with Hans Z. Munthe-Kaas, Ari Stern, Olivier Verdier, SIAM Journal on Applied Algebra and Geometry (2020).
- Lie-Butcher Series, Geometry, Algebra and Computation, with Hans Z. Munthe-Kaas, Kristoffer K. Føllesdal, Discrete Mechanics, Geometric Integration and Lie-Butcher Series (Springer) (2018).
- Pre- and Post-Lie Algebras: The Algebro-Geometric View, with Gunnar Fløystad, Hans Z. Munthe-Kaas, The Abel Symposium 2016 (Springer) (2018).
- Post-Lie Algebras and Factorization Theorems, with Kurusch Ebrahimi-Fard, Igor Mencattini, Hans Z. Munthe-Kaas, Journal of Geometry and Physics (2017).
- B-series Methods Are Exactly the Affine Equivariant Methods, with Robert I. McLachlan, Klas Modin, Hans Z. Munthe-Kaas, Olivier Verdier, Numerische Mathematik (2016).
- Aromatic Butcher Series, with Hans Z. Munthe-Kaas, Olivier Verdier, Foundations of Computational Mathematics (2016).