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TU Berlin

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Forschung

Research Alexander Schmeding

My main research interests are infinite-dimensional (differential) geometry, global analysis and Lie theory. Together with other researchers from the research group of Prof. P. Friz, I am working on applications of infinite-dimensional geometry to the theory of rough paths and stochastic (partial) differential equations.

Rough path theory is in itself already quite geometric and can be formulated with ease in a Banach space setting. However, then geometric, combinatorial and topological questions come into play. 

My research interests and expertise encompass in particular topologies on spaces of (smooth) functions,  diffeomorphism groups and higher categories in differential geometry (in the form of Lie groupoids) and their connections to infinite-dimensional geometry.

Before joining the group in Berlin I have worked several years at NTNU Trondheim (for example in the EU-project CHiPS). There applications of infinite-dimensional geometry and numerical analysis were key elements of my research. If you want to know more, (almost) all of my preprints can be found on the arXiv in preprint form.

Here are some key research areas I am interested in (together with some of my contributions):

Infinite-dimensional Geometry, rough paths and stochastic analysis

Rough paths are connected to character groups of certain Hopf algebras (see here for an explanation).
These groups turn out to be infinite-dimensional Lie groups:

Shape Analysis (on spaces with ambient geometry)

cf. the survey ''Shape analysis on Lie groups and homogeneous spaces'' 

Geometry on manifolds of Differentiable mappings

Lie groupoids vs. Infinite-dimensional Lie groups

Linking Lie groupoids and infinite-dimensional Lie groups.

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