2025-07-24 –, Main Room 6
Manifolds are mathematical objects that can be used to describe complicated numerical domains. They are often used in optimization, statistical computations, physics and engineering. Manifolds can describe constraints on data, be used to explore necessity of assumptions in numerical algorithms or design faster algorithms. The talk provides an overview of the capabilities available in JuliaManifolds and beyond, along with a historical perspective and future prospects.
The following aspects of manifolds in numerical computing will be discussed in the talk:
- New developments in JuliaManifolds for robotics, including a work-in-progress library for geometric Kalman filters, focusing on affine connections.
- Viability of Manopt.jl as a general-purpose optimization framework. Highlights include comprehensive solver availability, ability to work with arbitrarily structured decision variables and performance.
- Ongoing development of statistical tools on manifolds: both methods that work with manifold-valued data as well as methods that exploit manifold structure implicit in the problem, with examples such as robust principal component analysis. Rapid prototyping of advanced optimization-based models.
- Perspectives of new developments: stratification as a tool for mixing continuous and discrete data, manifolds with corners for more expressive constraints.
The talk only assumes basic knowledge of linear algebra, multivariate calculus and ordinary differential equations.
Assistant professor at AGH University of Krakow. I work on numerical differential geometry and biomedical engineering.