40 citations · 295 across the 45 of their papers we have counts for
49 papers
Metric Geometry of the Signature Group for -Variation Rough Paths
Felix Medwed, Sylvie Paycha, Alexander Schmeding
The signatures of -rough paths form a subgroup of sufficiently high-level truncated tensor algebras, whose inverse limit is a subgroup of the full tensor algebra. For …
Flows and Homotopies of Banach Lie algebroids
Fernand Pelletier, Alexander Schmeding
We establish flow and homotopy tools for Banach Lie algebroids that do not rely on compactly supported extensions. Under suitable hypotheses, we construct parameter-dependent local…
Optimization on Weak Riemannian Manifolds
Valentina Zalbertus, Max Pfeffer, Alexander Schmeding
Riemannian structures on infinite-dimensional manifolds arise naturally in shape analysis and shape optimization. These applications lead to optimization problems on manifolds whic…
Group Contractions via Infinite-Dimensional Lie Theory
David Prinz, Alexander Schmeding, Philip K. Schwartz
Contractions are a procedure to construct a new Lie algebra out of a given one via a singular limit. Specifically, the İnönü--Wigner construction starts with a Lie algebra $\mathfr…
Cotangent Bundles as Coadjoint Orbits and Asymptotic Character Formulas
Michael Gjertsen, Alexander Schmeding
We present geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjoint orbit of an in…
The Stacey-Roberts Lemma for Banach Manifolds
Peter Kristel, Alexander Schmeding
The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by…
On the singularities of the exponential function of a semidirect product
Alexandru Chirvasitu, Rafael Dahmen, Karl-Hermann Neeb +1
We show that the Fréchet--Lie groups of the form resulting from smooth flows on compact manifolds fail to be locally exponential in several ca…
Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups
Helge Glockner, Alexander Schmeding, Ali Suri
We construct a smooth Banach manifold BV whose elements are suitably-defined functions of bounded variation with values in a smooth Banach manif…
Boundary values of diffeomorphisms of simple polytopes, and controllability
Helge Glöckner, Erlend Grong, Alexander Schmeding
We consider the Lie group of smooth diffeomorphisms Diff of a simple polytope in the euclidean space. Simple polytopes are special cases of manifolds with corners. The geo…
Controllability and diffeomorphism groups on manifolds with boundary
Erlend Grong, Alexander Schmeding
In this article we consider diffeomorphism groups of manifolds with smooth boundary. We show that the diffeomorphism groups of the manifold and its boundary fit into a short exact…
The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations
Zdzisław Brzeźniak, Mario Maurelli, Alexander Schmeding
The Ebin-Marsden theory is a powerful geometric framework for many PDEs from fluid dynamics. In this paper we provide a toolbox to apply the Ebin-Marsden approach to stochastic PDE…
Decompositions of Nonlinear Input-Output Systems to Zero the Output
W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding
Consider an input-output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact…
On the unit component of the Newman-Unti group
Alexander Schmeding
In this short note we identify the unit component of the Newman--Unti (NU) group in the fine very strong topology. In previous work, this component has been endowed with an infinit…
Deep neural networks on diffeomorphism groups for optimal shape reparameterization
Elena Celledoni, Helge Glöckner, Jørgen Riseth +1
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization rea…
A topological splitting of the space of meromorphic germs in several variables and continuous evaluators
Rafael Dahmen, Sylvie Paycha, Alexander Schmeding
We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs.…
The geometry of controlled rough paths
Mazyar Ghani Varzaneh, Sebastian Riedel, Alexander Schmeding +1
We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dime…
An introduction to infinite-dimensional differential geometry
Alexander Schmeding
The present document is the draft of a book which presents an introduction to infinite-dimensional differential geometry beyond Banach manifolds. As is well known the usual calculu…
Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group
David Prinz, Alexander Schmeding
We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a…
Manifolds of mappings on cartesian products
Helge Glockner, Alexander Schmeding
Given smooth manifolds (which may have a boundary or corners), a smooth manifold modeled on locally convex spaces and , w…
Lie Theory for Asymptotic Symmetries in General Relativity: The BMS Group
David Prinz, Alexander Schmeding
We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric defin…
Continuity of Formal Power Series Products in Nonlinear Control Theory
W. Steven Gray, Mathias Palmstrøm, Alexander Schmeding
Formal power series products appear in nonlinear control theory when systems modeled by Chen-Fliess series are interconnected to form new systems. In fields like adaptive control a…
Geometric rough paths on infinite dimensional spaces
Erlend Grong, Torstein Nilssen, Alexander Schmeding
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For , we give criteria for whe…
Continuity of Chen-Fliess Series for Applications in System Identification and Machine Learning
Rafael Dahmen, W. Steven Gray, Alexander Schmeding
Model continuity plays an important role in applications like system identification, adaptive control, and machine learning. This paper provides sufficient conditions under which i…
Incompressible Euler equations with stochastic forcing: a geometric approach
Mario Maurelli, Klas Modin, Alexander Schmeding
We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact m…