# Current projects

## Main content

Name | Period | Core members |

GeoProCo: Geometry and Probability with constrains | 2021-2025 | Erlend Grong, Sylvie Vega-Molino, Francesco Ballerin |

CODYSMA: Computational Dynamics and Stochastics on Manifolds | 2020-2025 | Hans Z. Munthe-Kaas, Jonatan Stava |

TMS-Pure Math in Norway | 2018-2025 | The math departments at UiB, UiO, NTNU and UiT |

Nonlinear Dispersive Equations | 2018-2024 | Didier Pilod, Martin Oen Paulsen, Torunn Stavland Jensen |

## GeoProCo

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. Website

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

## CODYSMA

The project CODYSMA: Computational Dynamics and Stochastics on Manifolds is a five year project which started January 1st, 2020 supported by the Norwegian Research Council through the program FRIPRO. The objective of the project is to provide the mathematical community with new mathematical theories and software tools for analysis and computations on manifolds. Website

## TMS-Pure Math in Norway

Funded by the Trond Mohn Foundation. The main aim of the project is to strengthen research in pure mathematics in Norway, by contributing to national and international research collaboration, mobility of researchers and Ph.D. students, and training of Ph.D and master students. It started on May 1, 2018 and would originally run for four years. It has been extended for three more years, until 30 April 2025. The Principal Coordinators are Sigmund Selberg (2018-2022) and Gunnar Fløystad (2022-2024). Website

## Nonlinear Dispersive Equations

The research project "Nonlinear dispersive equations: nonlocal operators, dispersive blow-up and the soliton resolution conjecture" (NonDispEq) is founded by the Trond Mohn Stiftelse (TMS) and hosted at the Department of Mathematics of the University of Bergen. It was launched in 2018 and aims at expanding our knowledge of dynamic properties of solutions to nonlinear dispersive evolution equations arising in mathematical physics and mathematical fluid mechanics. Website