The PhD project offers multiple research directions where one can develop and apply novel state-of-art computational methods, including: Generalising algorithms, to Riemannian manifolds and investigating their properties like convergence or a convergence rate; Investigate properties of models, like total generalised variation (TGV) regularisation, for manifold-valued data; Numerical investigation of the developed algorithms, for example to shape optimisation or manifold-valued data processing; Investigating further applications towards automatic differentiation or machine learning for manifold-valued data and optimisation on manifolds
Theoretical Knowledge in Differential Geometry, Convex Analysis and Data Processing, for example Image Processing; Experience in programming numerical methods is highly desirable, in particular knowledge and experience with programming languages, preferably Julia or Python; Experience with Open Source packages and their development is a plus but not required; Good language skills: Written and oral in English and if possible Norwegian skills
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