Alexander Schmeding

Om

Matematiker interessert i uendelig dimensjonal differensialgeometri, Lie teori og deres anvendelse. Utover forskning i ren og anvendt matematikk er jeg også interessert i matematikkdidaktikk (spesielt knyttet til høyere utdanning og lærerutdanninger).

Jeg er ansvarlig for koordinering av EVU aktivitetene ved IMF.

Bakgrunn

Jeg oppnådde min Doktorgrad (den tyske ekvivalenten til PhD) i uendelig dimensjonal Lie teori ved Universitetet i Paderborn, Tyskland i 2013. Før fullførte jeg både et diplom i matematikk (i dag tilsvarer det en mastergrad i matematikk) og et lærerutdanningsprogram (matematikk og historie) ved universitetet i Paderborn. Etter det var jeg postdoktor ved NTNU, TU Berlin og middlertidig førsteamanuensis ved Universitetet i Bergen. Før jeg begynte på NTNU var jeg førsteamanuensis ved Nord universitet i Levanger hvor jeg jobbet flere år i lærerutdanningen.

Forskning

My research centers around infinite-dimensional differential geometry, Lie theory and their applications. Infinite-dimensional Lie groups arise naturally for example in the theory of hydrodynamics. The flow of a fluid particle (under periodic boundary conditions) can be modelled as a curve taking values in the group of volume preserving diffeomorphism on the torus. The resulting curve turns out to be connected to Riemannian geometry on the infinite-dimensional Lie group of volume preserving diffeomorphisms. Hence infinite-dimensional geometric tools and insights can be used to study flows in hydrodynamics. This example shows one of the subtle connections between finite and infinite-dimensional geometry I am interested in.

Beyond research in geometry, I am also interested in questions connected to the didactics of mathematics related to higher education at the university level and teacher education.

Research interests (mathematics)

Lie groups of diffeomorphisms
Lie groupoids and their representations
manifolds of mappings
(weak) Riemannian geometry on infinite-dimensional spaces
Interactions of differential geometry with rough path theory and Hopf algebras
Applications of the above (e.g. Geometric hydrodynamics and shape analysis)

Research interests (didactics of mathematics)

programming in mathematics textbooks for norwegian schools
peer- and self-evaluation activities in higher education

CODYSMA project

The project CODYSMA: Computational Dynamics and Stochastics on Manifolds is a five year project which started January 1st, 2020 supported by the Norwegian Research Council through the program FRIPRO.

Lie groups and manifolds of non-smooth mappings

We propose to construct and study Lie groups of paths of bounded variation with values in a Lie group. The driving motivation comes from the theory of rough paths. Rough path theory provides a fresh look at differential equations driven by rough signals.

Publikasjoner

An Introduction to Infinite-Dimensional Differential Geometry

Introducing foundational concepts in infinite-dimensional differential geometry, this book focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry. Available as Open Access.

Errata for "An Introduction to infinite-dimensional Differential Geometry"

Unfortunately, no publication without errors. Here is a list of all known errata for the book on infinite-dimensional geometry by CUP.

Nesten alle mine matematiske publikasjoner er på arXiv. Grunnleggende informasjoner om forskningen min finnes i boka "An introduction to infinite-dimensional differential geometry". Boka er publisert som open access ved Cambridge University Press.

For artikler i matematikkdidaktik sjekk Researchgate.

2024

Gray, W. Steven; Ebrahimi-Fard, Kurusch; Schmeding, Alexander. (2024) Decompositions of nonlinear input–output systems to zero the output. Systems & control letters (Print)
Vitenskapelig artikkel
Dahmen, Rafael; Paycha, Sylvie; Schmeding, Alexander. (2024) A topological splitting of the space of meromorphic germs in several variables and continuous evaluators. Complex Analysis and its Synergies
Vitenskapelig artikkel
Grong, Erlend; Schmeding, Alexander. (2024) Controllability and diffeomorphism groups on manifolds with boundary. Forum mathematicum
Vitenskapelig artikkel
Gray, W Steven; Pham, Natalie; Schmeding, Alexander. (2024) Distributional Generating Series in Nonlinear Control Theory. IEEE conference proceedings
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel

2023

Schmeding, Alexander. (2023) On the unit component of the Newman-Unti group. Classical and Quantum Gravity
Vitenskapelig artikkel
Celledoni, Elena; Glöckner, Helge; Riseth, Jørgen Nilsen; Schmeding, Alexander. (2023) Deep neural networks on diffeomorphism groups for optimal shape reparametrization. BIT Numerical Mathematics
Vitenskapelig artikkel
Maurelli, Mario; Modin, Klas; Schmeding, Alexander. (2023) Incompressible Euler equations with stochastic forcing: A geometric approach. Stochastic Processes and their Applications
Vitenskapelig artikkel
Gray, W. Steven; Ebrahimi-Fard, Kurusch; Schmeding, Alexander. (2023) Zeroing the Output of Nonlinear Systems Without Relative Degree. IEEE conference proceedings
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Jensen, Mari Solberg; Julien, Antoine Laurent Christophe; Rafiepour, Abolfazl; Schmeding, Alexander. (2023) An analytical framework for programming tasks in mathematics textbooks. European Society for Research in Mathematics Education
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Jensen, Mari Solberg; Schmeding, Alexander. (2023) Jupyter notatbok i programmering. Tangenten - Tidsskrift for matematikkundervisning
Fagartikkel

2022

Prinz, David Nicolas; Schmeding, Alexander. (2022) Lie theory for asymptotic symmetries in general relativity: The BMS Group. Classical and Quantum Gravity
Vitenskapelig artikkel
Glöckner, Helge; Schmeding, Alexander. (2022) Manifolds of mappings on Cartesian products. Annals of Global Analysis and Geometry
Vitenskapelig artikkel
Gray, W. Steven; Palmstrøm, Mathias; Schmeding, Alexander. (2022) Continuity of Formal Power Series Products in Nonlinear Control Theory. Foundations of Computational Mathematics
Vitenskapelig artikkel
Julien, Antoine Laurent Christophe; Romijn, Elisabeth Inge; Schmeding, Alexander. (2022) Peer and self-assessment to improve mathematics competence in pre-service middle-school teachers. European Society for Research in Mathematics Education
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Prinz, David Nicolas; Schmeding, Alexander. (2022) Lie theory for asymptotic symmetries in general relativity: The NU group. Classical and Quantum Gravity
Vitenskapelig artikkel
Schmeding, Alexander. (2022) An Introduction to Infinite-Dimensional Differential Geometry. Cambridge University Press Cambridge Studies in Advanced Mathematics
Vitenskapelig monografi
Grong, Erlend; Nilssen, Torstein; Schmeding, Alexander. (2022) Geometric rough paths on infinite dimensional spaces. Journal of Differential Equations
Vitenskapelig artikkel

2021

Dahmen, Rafael; Gray, W. Steven; Schmeding, Alexander. (2021) Continuity of Chen-Fliess Series for Applications in System Identification and Machine Learning. IFAC-PapersOnLine
Vitenskapelig artikkel
Roberts, David M.; Schmeding, Alexander. (2021) Extending Whitney's extension theorem: nonlinear function spaces. Annales de l'Institut Fourier
Vitenskapelig artikkel
Schmeding, Alexander. (2021) Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application. John Wiley & Sons
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Schmeding, Alexander. (2021) Applications of inﬁnite-dimensional geometry and Lie theory Habilitationsschrift. Technische Universität Berlin
Doktorgradsavhandling
Ebrahimi-Fard, Kurusch; Gray, W. Steven; Schmeding, Alexander. (2021) Universal Zero Dynamics: The SISO Case. IEEE (Institute of Electrical and Electronics Engineers) IEEE (Institute of Electrical and Electronics Engineers)
Rapport

2020

Schmeding, Alexander; Amiri, Habib; Glöckner, Helge. (2020) Lie groupoids of mappings taking values in a Lie groupoid. Archivum mathematicum
Vitenskapelig artikkel
Schmeding, Alexander; Dahmen, Rafael. (2020) Lie groups of controlled characters of combinatorial Hopf algebras. Annales de l’Institut Henri Poincaré D (AIHPD)
Vitenskapelig artikkel

2019

Schmeding, Alexander. (2019) The Lie group of vertical bisections of a regular Lie groupoid. Forum mathematicum
Vitenskapelig artikkel
Amiri, Habib; Schmeding, Alexander. (2019) A Differentiable Monoid of Smooth Maps on Lie Groupoids. Journal of Lie theory
Vitenskapelig artikkel
Curry, Charles Henry Alexander; Schmeding, Alexander. (2019) Convergence of Lie group integrators. Numerische Mathematik
Vitenskapelig artikkel

2018

Celledoni, Elena; Eidnes, Sølve; Schmeding, Alexander. (2018) Shape analysis on homogeneous spaces: a generalised SRVT framework. Abel Symposia
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2018) The geometry of characters of hopf algebras. Abel Symposia
Vitenskapelig artikkel

2017

Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus; Schmeding, Alexander. (2017) Shape analysis on Lie groups and homogeneous manifolds. Proceedings of the GSI conference 2017
Sammendrag/abstract
Schmeding, Alexander; Hjelle, Eivind Otto. (2017) Strong topologies for spaces of smooth maps with infinite-dimensional target. Expositiones mathematicae
Vitenskapelig artikkel
Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus; Schmeding, Alexander. (2017) Shape analysis on lie groups and homogeneous spaces. Lecture Notes in Computer Science (LNCS)
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2017) The Lie Group Structure of the Butcher Group. Foundations of Computational Mathematics
Vitenskapelig artikkel

2016

Bogfjellmo, Geir; Dahmen, Rafael; Schmeding, Alexander. (2016) Character groups of Hopf algebras as infinite-dimensional Lie groups. Annales de l'Institut Fourier
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2016) Functorial aspects of the reconstruction of Lie groupoids from their bisections. Journal of the Australian Mathematical Society
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2016) The tame Butcher group. Journal of Lie theory
Vitenskapelig artikkel
Celledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Shape analysis on Lie groups with application in computer animation. Journal of Geometric Mechanics (JGM)
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2016) (Re)constructing Lie groupoids from their bisections and applications to prequantisation. Differential geometry and its applications
Vitenskapelig artikkel

2015

Dahmen, Rafael; Schmeding, Alexander. (2015) The Lie group of real analytic diffeomorphisms is not real analytic. Studia Mathematica
Vitenskapelig artikkel
Schmeding, Alexander. (2015) The diffeomorphism group of a non-compact orbifold. Dissertationes Mathematicae
Vitenskapelig artikkel
Schmeding, Alexander; Alzaareer, Hamza. (2015) Differentiable mappings on products with different degrees of differentiability in the two factors. Expositiones mathematicae
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2015) The Lie group of bisections of a Lie groupoid. Annals of Global Analysis and Geometry
Vitenskapelig artikkel

Tidsskriftspublikasjoner

Gray, W. Steven; Ebrahimi-Fard, Kurusch; Schmeding, Alexander. (2024) Decompositions of nonlinear input–output systems to zero the output. Systems & control letters (Print)
Vitenskapelig artikkel
Dahmen, Rafael; Paycha, Sylvie; Schmeding, Alexander. (2024) A topological splitting of the space of meromorphic germs in several variables and continuous evaluators. Complex Analysis and its Synergies
Vitenskapelig artikkel
Grong, Erlend; Schmeding, Alexander. (2024) Controllability and diffeomorphism groups on manifolds with boundary. Forum mathematicum
Vitenskapelig artikkel
Schmeding, Alexander. (2023) On the unit component of the Newman-Unti group. Classical and Quantum Gravity
Vitenskapelig artikkel
Celledoni, Elena; Glöckner, Helge; Riseth, Jørgen Nilsen; Schmeding, Alexander. (2023) Deep neural networks on diffeomorphism groups for optimal shape reparametrization. BIT Numerical Mathematics
Vitenskapelig artikkel
Maurelli, Mario; Modin, Klas; Schmeding, Alexander. (2023) Incompressible Euler equations with stochastic forcing: A geometric approach. Stochastic Processes and their Applications
Vitenskapelig artikkel
Jensen, Mari Solberg; Schmeding, Alexander. (2023) Jupyter notatbok i programmering. Tangenten - Tidsskrift for matematikkundervisning
Fagartikkel
Prinz, David Nicolas; Schmeding, Alexander. (2022) Lie theory for asymptotic symmetries in general relativity: The BMS Group. Classical and Quantum Gravity
Vitenskapelig artikkel
Glöckner, Helge; Schmeding, Alexander. (2022) Manifolds of mappings on Cartesian products. Annals of Global Analysis and Geometry
Vitenskapelig artikkel
Gray, W. Steven; Palmstrøm, Mathias; Schmeding, Alexander. (2022) Continuity of Formal Power Series Products in Nonlinear Control Theory. Foundations of Computational Mathematics
Vitenskapelig artikkel
Prinz, David Nicolas; Schmeding, Alexander. (2022) Lie theory for asymptotic symmetries in general relativity: The NU group. Classical and Quantum Gravity
Vitenskapelig artikkel
Grong, Erlend; Nilssen, Torstein; Schmeding, Alexander. (2022) Geometric rough paths on infinite dimensional spaces. Journal of Differential Equations
Vitenskapelig artikkel
Dahmen, Rafael; Gray, W. Steven; Schmeding, Alexander. (2021) Continuity of Chen-Fliess Series for Applications in System Identification and Machine Learning. IFAC-PapersOnLine
Vitenskapelig artikkel
Roberts, David M.; Schmeding, Alexander. (2021) Extending Whitney's extension theorem: nonlinear function spaces. Annales de l'Institut Fourier
Vitenskapelig artikkel
Schmeding, Alexander; Amiri, Habib; Glöckner, Helge. (2020) Lie groupoids of mappings taking values in a Lie groupoid. Archivum mathematicum
Vitenskapelig artikkel
Schmeding, Alexander; Dahmen, Rafael. (2020) Lie groups of controlled characters of combinatorial Hopf algebras. Annales de l’Institut Henri Poincaré D (AIHPD)
Vitenskapelig artikkel
Schmeding, Alexander. (2019) The Lie group of vertical bisections of a regular Lie groupoid. Forum mathematicum
Vitenskapelig artikkel
Amiri, Habib; Schmeding, Alexander. (2019) A Differentiable Monoid of Smooth Maps on Lie Groupoids. Journal of Lie theory
Vitenskapelig artikkel
Curry, Charles Henry Alexander; Schmeding, Alexander. (2019) Convergence of Lie group integrators. Numerische Mathematik
Vitenskapelig artikkel
Celledoni, Elena; Eidnes, Sølve; Schmeding, Alexander. (2018) Shape analysis on homogeneous spaces: a generalised SRVT framework. Abel Symposia
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2018) The geometry of characters of hopf algebras. Abel Symposia
Vitenskapelig artikkel
Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus; Schmeding, Alexander. (2017) Shape analysis on Lie groups and homogeneous manifolds. Proceedings of the GSI conference 2017
Sammendrag/abstract
Schmeding, Alexander; Hjelle, Eivind Otto. (2017) Strong topologies for spaces of smooth maps with infinite-dimensional target. Expositiones mathematicae
Vitenskapelig artikkel
Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus; Schmeding, Alexander. (2017) Shape analysis on lie groups and homogeneous spaces. Lecture Notes in Computer Science (LNCS)
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2017) The Lie Group Structure of the Butcher Group. Foundations of Computational Mathematics
Vitenskapelig artikkel
Bogfjellmo, Geir; Dahmen, Rafael; Schmeding, Alexander. (2016) Character groups of Hopf algebras as infinite-dimensional Lie groups. Annales de l'Institut Fourier
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2016) Functorial aspects of the reconstruction of Lie groupoids from their bisections. Journal of the Australian Mathematical Society
Vitenskapelig artikkel
Bogfjellmo, Geir; Schmeding, Alexander. (2016) The tame Butcher group. Journal of Lie theory
Vitenskapelig artikkel
Celledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Shape analysis on Lie groups with application in computer animation. Journal of Geometric Mechanics (JGM)
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2016) (Re)constructing Lie groupoids from their bisections and applications to prequantisation. Differential geometry and its applications
Vitenskapelig artikkel
Dahmen, Rafael; Schmeding, Alexander. (2015) The Lie group of real analytic diffeomorphisms is not real analytic. Studia Mathematica
Vitenskapelig artikkel
Schmeding, Alexander. (2015) The diffeomorphism group of a non-compact orbifold. Dissertationes Mathematicae
Vitenskapelig artikkel
Schmeding, Alexander; Alzaareer, Hamza. (2015) Differentiable mappings on products with different degrees of differentiability in the two factors. Expositiones mathematicae
Vitenskapelig artikkel
Schmeding, Alexander; Wockel, Christoph. (2015) The Lie group of bisections of a Lie groupoid. Annals of Global Analysis and Geometry
Vitenskapelig artikkel

Bøker

Schmeding, Alexander. (2022) An Introduction to Infinite-Dimensional Differential Geometry. Cambridge University Press Cambridge Studies in Advanced Mathematics
Vitenskapelig monografi

Del av bok/rapport

Gray, W Steven; Pham, Natalie; Schmeding, Alexander. (2024) Distributional Generating Series in Nonlinear Control Theory. IEEE conference proceedings
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Gray, W. Steven; Ebrahimi-Fard, Kurusch; Schmeding, Alexander. (2023) Zeroing the Output of Nonlinear Systems Without Relative Degree. IEEE conference proceedings
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Jensen, Mari Solberg; Julien, Antoine Laurent Christophe; Rafiepour, Abolfazl; Schmeding, Alexander. (2023) An analytical framework for programming tasks in mathematics textbooks. European Society for Research in Mathematics Education
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Julien, Antoine Laurent Christophe; Romijn, Elisabeth Inge; Schmeding, Alexander. (2022) Peer and self-assessment to improve mathematics competence in pre-service middle-school teachers. European Society for Research in Mathematics Education
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
Schmeding, Alexander. (2021) Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application. John Wiley & Sons
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel

Rapport

Schmeding, Alexander. (2021) Applications of inﬁnite-dimensional geometry and Lie theory Habilitationsschrift. Technische Universität Berlin
Doktorgradsavhandling
Ebrahimi-Fard, Kurusch; Gray, W. Steven; Schmeding, Alexander. (2021) Universal Zero Dynamics: The SISO Case. IEEE (Institute of Electrical and Electronics Engineers) IEEE (Institute of Electrical and Electronics Engineers)
Rapport

Undervisning

Vår 2024

TMA4115 - Matematikk 3

Høst 2024

MA3407 - Introduksjon til Lie-teori

MA3001 - Introduction to Riemannian geometry

Veiledning

Hvis du er interessert i å ta en oppgave eller et prosjekt med meg, vennligst ta kontakt. Jeg fører en liste med mulige tema som passer for prosjekter knyttet til mine forskningsinteresser i matematikk (se Forskningssiden).

Jeg kan også veilede oppgaver i matematikkdidaktikk (tema i didaktikk er for det meste knyttet Tril lærebokanalyse, programmering og digitale verktøy i matematikkundervisning).

Formidling