publications by categories in reversed chronological order

slides for conference talks:


  1. K. Modin, and M. Roop
    Spatio-temporal Lie-Poisson discretization for incompressible magnetohydrodynamics on the sphere
  2. K. Modin, and M. Perrot
    Eulerian and Lagrangian stability in Zeitlin’s model of hydrodynamics
  3. E. Jansson, and K. Modin
    Geometric discretization of diffeomorphisms
  4. E. Jansson, and K. Modin
    Sub-Riemannian landmark matching and its interpretation as residual neural networks

peer-reviewed articles


  1. K. Modin
    On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport
    J. Comput. Dyn. (accepted), 2024
  2. B. KhesinK. Modin, and L. Volk
    Simple unbalanced optimal transport
    Int. Math. Res. Not., 2024


  1. E. Jansson, and K. Modin
    Convergence of the vertical gradient flow for the Gaussian Monge problem
    J. Comput. Dyn., 2023
  2. B. Khesin, and K. Modin
    The Toda flow as a porous medium equation
    Comm. Math. Phys., 2023
  3. M. MaurelliK. Modin, and A. Schmeding
    Incompressible Euler equations with stochastic forcing: a geometric approach
    Stochastic Process. Appl., 2023
  4. P. CifaniM. Viviani, and K. Modin
    An efficient geometric method for incompressible hydrodynamics on the sphere
    J. Comput. Phys., 2023


  1. T. Balehowsky, C-J. Karlsson, and K. Modin
    Shape analysis via gradient flows on diffeomorphism groups
    Nonlinearity, 2022
  2. P. CifaniM. VivianiE. LuesinkK. Modin, and B. Geurts
    Casimir preserving spectrum of two-dimensional turbulence
    Phys. Rev. Fluids, 2022
  3. K. Modin, and M. Viviani
    Canonical scale separation in two-dimensional incompressible hydrodynamics
    J. Fluid Mech., 2022


  1. B. KhesinG. Misiolek, and K. Modin
    Geometric hydrodynamics and infinite-dimensional Newton’s equations
    Bull. Amer. Math. Soc., 2021
  2. K. Modin, and M. Viviani
    Integrability of point-vortex dynamics via symplectic reduction: a survey
    Arnold Math. J., 2021


  1. K. Modin, and O. Verdier
    What makes nonholonomic integrators work?
    Numer. Math., 2020
  2. M. Bauer, and K. Modin
    Semi-invariant Riemannian metrics in hydrodynamics
    Calc. Var. Partial Differential Equations, 2020
  3. K. Modin, and M. Viviani
    A Casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics
    J. Fluid Mech., 2020
  4. K. Modin, and M. Viviani
    Lie-Poisson methods for isospectral flows
    Found. Comput. Math., 2020


  1. J. BennS. MarslandR. McLachlanK. Modin, and O. Verdier
    Currents and finite elements as tools for shape space
    J. Math. Imaging Vis., 2019
  2. B. KhesinG. Misiolek, and K. Modin
    Geometry of the Madelung transform
    Arch. Ration. Mech. Anal., 2019
  3. J. Hellsvik, D. Thonig, K. Modin, D. Iusan, A. Bergman, O. Eriksson, L. Bergqvist, and A. Delin
    General method for atomistic spin-lattice dynamics with first-principles accuracy
    Phys. Rev. B, 2019


  1. K. ModinA. Nachman, and L. Rondi
    A Multiscale Theory for Image Registration and Nonlinear Inverse Problems
    Adv. Math., 2018
  2. G. BogfjellmoK. Modin, and O. Verdier
    A Numerical Algorithm for C2-splines on Symmetric Spaces
    SIAM J. Numer. Analysis, 2018
  3. B. KhesinG. Misiolek, and K. Modin
    Geometric Hydrodynamics via Madelung Transform
    Proc. Natl. Acad. Sci. USA, 2018


  1. M. BauerS. Joshi, and K. Modin
    Diffeomorphic random sampling using optimal information transport
    In Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science, vol 10589. Springer, 2017
  2. M. BauerS. Joshi, and K. Modin
    On Geodesic Completeness of Riemannian Metrics on Smooth Probability Densities
    Calc. Var. Partial Differential Equations, 2017
  3. K. Modin
    Geometry of Matrix Decompositions Seen Through Optimal Transport and Information Geometry
    J. Geom. Mech., 2017
  4. R. McLachlanK. ModinH. Munthe-Kaas, and O. Verdier
    Butcher series: A story of rooted trees and numerical methods for evolution equations
    Asia Pacific Mathematics Newsletter, 2017
  5. R. McLachlanK. Modin, and O. Verdier
    A minimal-variable symplectic integrator on spheres
    Math. Comp., 2017


  1. R. McLachlanK. Modin, and O. Verdier
    Symmetry reduction for central force problems
    Eur. J. Phys., 2016
  2. R. McLachlanK. Modin, and O. Verdier
    Geometry of discrete-time spin systems
    J. Nonlin. Sci., 2016
  3. R. McLachlanK. ModinH. Munthe-Kaas, and O. Verdier
    B-series methods are exactly the affine equivariant methods
    Numer. Math., 2016


  1. C. Rottman, M. BauerK. Modin, and S. Joshi
    Weighted Diffeomorphic Density Matching with Applications to Thoracic Image Registration
    In Proc. 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA), Munich, Germany, October 9, 2015
  2. M. BauerS. Joshi, and K. Modin
    Diffeomorphic density matching by optimal information transport
    SIAM J. Imaging Sci., 2015
  3. R. McLachlanK. Modin, and O. Verdier
    Collective Lie-Poisson integrators on R3
    IMA. J. Num. Anal., 2015
  4. K. Modin
    Generalized Hunter-Saxton equations, optimal information transport, and factorization of diffeomorphisms
    J. Geom. Anal., 2015


  1. R. McLachlanK. Modin, and O. Verdier
    Symplectic integrators for spin systems
    Phys. Rev. E, 2014
  2. R. McLachlanK. Modin, and O. Verdier
    Collective symplectic integrators
    Nonlinearity, 2014
  3. S. MarslandR. McLachlanK. Modin, and M. Perlmutter
    On conformal variational problems and free boundary continua
    J. Phys. A, 2014
  4. R. McLachlanK. ModinO. Verdier, and M. Wilkins
    Geometric Generalisations of SHAKE and RATTLE
    Found. Comput. Math., 2014


  1. R. McLachlanK. ModinO. Verdier, and M. Wilkins
    Symplectic integrators for index 1 constraints
    SIAM J. Sci. Comput., 2013
  2. K. Modin, and O. Verdier
    Integrability of Nonholonomically Coupled Oscillators
    Discrete Contin. Dyn. Syst., 2013
  3. S. MarslandR. McLachlanK. Modin, and M. Perlmutter
    Geodesic Warps by Conformal Mappings
    Int. J. Comput. Vis., 2013


  1. S. MarslandR. McLachlanK. Modin, and M. Perlmutter
    On a Geodesic Equation for Planar Conformal Template Matching
    In Proc. MFCA’11, 2011
  2. K. Modin, and G. Söderlind
    Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping
    BIT Num. Math., 2011
  3. K. ModinM. PerlmutterS. Marsland, and R. McLachlan
    On Euler-Arnold Equations and Totally Geodesic Subgroups
    J. Geom. Phys., 2011


  1. K. Modin
    Time-transformation and reversibility of Nambu-Poisson systems
    J. Gen. Lie Theory Appl., 2009


  1. K. Modin
    On explicit adaptive symplectic integration of separable Hamiltonian systems
    J. Mult. Body Mech., 2008


  1. K. Modin, and C. Führer
    Time-step adaptivity in variational integrators with application to contact problems
    ZAMM Z. Angew. Math. Mech., 2006

book chapters

  1. K. Modin
    Geometric Hydrodynamics: from Euler, to Poincaré, to Arnold
    In 13th Young Researchers Workshop on Geometry, Mechanics and Control: Three Mini-courses, 2019
  2. M. BauerS. Joshi, and K Modin
    Diffeomorphic density registration
    In Riemannian Geometric Statistics in Medical Image Analysis, 2020
  3. K. Modin
    Adaptive Geometric Numerical Integration of Mechanical Systems
    Lund University, 2009

technical reports

  1. S. S. Larsson, T. Matsuo, K. Modin, and M. Molteni
    Discrete Variational Derivative Methods for the EPDiff Equation
  2. K. Modin
    Diffeomorphic density transport - a numerical challenge
    In Oberwolfach Rep. 13: Geometric Numerical Integration, 2016
  3. Proceedings of Math on the Rocks Shape Analysis Workshop in Grundsund
    Jul 2015
  4. K. ModinM. Perlmutter, S Marsland, and R. McLachlan
    Geodesics on Lie Groups: Euler Equations and Totally Geodesic Subgroups
    Jul 2010
  5. K. Modin
    Geometric integration of non-autonomous systems with application to rotor dynamics
    Jul 2009