We have a mature understanding of algorithms and complexity for flat Euclidean spaces, our simplest model of the geometry of the world we live in. Euclidean geometric algorithms form the foundations of modern computer graphics and vision, and they are used in several tasks in machine learning, robotics, and all computation that deals with the real world. However, the Euclidean world we experience directly is only a small slice of reality: relativity states that we live in a spacetime which is intimately tied to hyperbolic geometry. Recently we find that from machine learning to quantum physics hyperbolic geometry is indispensable. Unfortunately our computational understanding of hyperbolic geometry is still rudimentary, we lack the tools to efficiently process data that is hyperbolic. The goal of the project is to design and analyse fundamental geometric algorithms for hyperbolic spaces, laying the groundwork for future developments in such geometries.

2024

2028