From Geometry to Artificial Intelligence – Results from the TMF Starting Grant GeoProCo Project
The GeoProCo project – Geometry and Probability with Constraints – is now completed. It has been led by Associate Professor Erlend Grong at the Department of Mathematics, University of Bergen. The aim has been to connect geometry and probability theory, and to explore how these fields can provide new solutions to complex problems.
Among the most important results from the project are:
- New mathematical methods: The research group has developed new ways to analyze and compare geometric spaces, and has found solutions to problems that have been open in the field. This includes a new normalization for Cartan connections and contributions to the Gauss-Bonnet theorem for sub-Riemannian surfaces.
- Link between geometry and probability: The project has investigated how random movements behave in curved spaces, and developed tools to analyze such processes – with relevance for physics, finance, and machine learning.
- Practical algorithms for data analysis: New algorithms have been created for dimension reduction and for solving differential equations in a way that takes the geometry of the data into account. This is important for modern machine learning and image processing.
International collaboration and dissemination:
The project has resulted in 13 published scientific articles and 9 preprints submitted for review, and has brought together researchers from Norway, Europe, and the USA. The group has organized courses, seminars, and international conferences – and produced teaching materials that are available to students and researchers.
The project has also contributed to career development for those involved. Project leader Erlend Grong has secured a permanent position and has applied for promotion to professor.
