GeoProCo
A project in geometry, probability and geometric integration
Welcome to the homepage of the project GeoProCo: Geometry and Probability with constraints.
The project period is from April 2021 to March 2025. The project is funded by the Trond Mohn foundation and is given under the scheme TMS Starting Grant.
The research concerns the following topics.
Differential geometry
Differential geometry is the study of shapes. This concerns the shapes we can picture, and how we can use the intuition from those to understand the shape of higher dimensional objects that we cannot picture.
Probability theory
Probability theory is the study of random variables and probability distributions. The project will focus in particular on random variables changing with the passage of time and equations involving these.
Geometric integration
Geometric integration is focused on the study of numerical methods that preserves som underlying geometric property exactly. A way in which you can ask a computer to solve a problem without ruining the shape you are sure should be kept.
Constraints
All of the previous topics will be studied in a setting where there are nonholonomic constrains, meaning that there are restrictions on how something can move.
Core members of the project
Publications and preprints of the project
Accepted or published
Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion (arXiv:2305.02688)
Journal of Lie Theory 34 (2024), No. 2, 339-352
Erlend Grong, Hans Z. Munthe-Kaas and Jonatan StavaThe Prytz Connections (arXiv: 2309. 02174)
Journal of Computational Dynamics, 2024, 11(3): 318-335.
Geir Bogfjellmo, Charles Curry, and Sylvie Vega-MolinoHolonomy of H-Type foliations
Accepted to Contemporary Mathematics
Fabrice Baudoin and Sylvie Vega-MolinoMost probable flows for Kunita SDEs. (arXiv:2209.03868)
Appl Math Optim 89, 44 (2024)
Erlend Grong and Stefan SommerHarmonic maps into sub-Riemannian Lie groups (arXiv:2305.06096)
Communications in Analysis and Mechanics (2023), Volume 15, Issue 3: 515-532.
Erlend Grong and Irina MarkinaCurvature and the equivalence problem in sub-Riemannian geometry. (arXiv:2206.15123)
Arch. Math. (Brno) 58 (2022), no.5, 295–327.
Erlend GrongMost probable paths for anisotropic Brownian motions on manifolds (arXiv:2110.15634)
Foundations of Computational Mathematics (2022): 1-3
Erlend Grong and Stefan SommerGeometric rough paths on infinite dimensional spaces. (arXiv:2006.06362)
J. Differential Equations 340 (2022), 151–178.
Erlend Grong, Torstein Nilssen, Alexander SchmedingA horizontal Chern-Gauss-Bonnet formula on totally geodesic foliations (arXiv:2106.15558)
Ann. Global Anal. Geom. 61 (2022), no. 4, 759–776.
Fabrice Baudoin, Erlend Grong, Gianmarco Vega-Molino
Preprints
Score matching for sub-Riemannian bridge sampling (arXiv:2404.15258)
Erlend Grong, Karen Habermann, Stefan SommerControllability of shapes through Landmark Manifolds (arXiv:2403.08090)
Erlend Grong and Sylvie Vega-MolinoControllability and diffeomorphism groups on manifolds with boundary (arXiv:2403.12742)
Erlend Grong and Alexander SchmedingPrincipal subbundles for dimension reduction (arXiv:2307.03128)
Morten Akhøj, James Benn, Erlend Grong, Stefan Sommer, Xavier PennecGeometry of the Visual Cortex with Applications to Image Inpainting and Enhancement (arXiv:2308.07652)
Francesco Ballerin and Erlend GrongFiltered complexes and cohomologically equivalent subcomplexes (arXiv:2308.11353)
Erlend Grong and Francesca TripaldiVariations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling (arXiv:2212.07715)
Fabrice Baudoin, Erlend Grong, Robert Neel and Anton ThalmaierMost probable paths for developed processes. (arXiv:2211.15168)
Erlend Grong and Stefan SommerLocal Invariants and Geometry of the sub-Laplacian on H-type Foliations (arXiv:2209.02168)
Wolfram Bauer, Irina Markina, Abdellah Laaroussi, and Sylvie Vega-MolinoA sub-Riemannian Gauss-Bonnet theorem for surfaces in contact manifolds (arXiv:2204.03451)
Erlend Grong, Jorge Hidalgo, and Sylvie Vega-Molino
