Alexander Schmeding
About
Mathematician working on infinitedimensional differential geometry, Lie theory and their application. Beyond research in pure and applied mathematics I am also interested in mathematics didactics (especially connected to higher education and teacher education programs).
I am responsible for the coordination of the EVU activities at IMF.
Background
I obtained my Doktorgrad (the german equivalent of PhD) in infinitedimensional Lie theory at the University of Paderborn, Germany in 2013. Before, I completed both a diploma in mathematics (nowadays equivalent to a master) and a teacher training program (mathematics and history) at the university of Paderborn. After that I held postdoctoral positions at NTNU, TU Berlin and was substitute associate professor at the University of Bergen. Before joining NTNU I was associate professor at Nord university in Levanger were I worked several years in teacher education.
Research
My research centers around infinitedimensional differential geometry, Lie theory and their applications. Infinitedimensional 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 infinitedimensional Lie group of volume preserving diffeomorphisms. Hence infinitedimensional geometric tools and insights can be used to study flows in hydrodynamics. This example shows one of the subtle connections between finite and infinitedimensional 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 infinitedimensional 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 selfevaluation activities in higher education
CODYSMA project
Lie groups and manifolds of nonsmooth mappings
Publications
An Introduction to InfiniteDimensional Differential Geometry
Errata for "An Introduction to infinitedimensional Differential Geometry"
Almost all of my mathematical publications are available on the arXiv. I wrote a book containing an introduction to many concepts in infinitedimensional geometry I am interested in. It is available in open access at the publishers website (check link below).
My publications in didactics in mathematics can be found as preprints on Researchgate.
2024

Gray, W Steven;
Pham, Natalie;
Schmeding, Alexander.
(2024)
Distributional Generating Series in Nonlinear Control Theory.
IEEE conference proceedings
Academic chapter/article/Conference paper

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
Academic article

Gray, W. Steven;
EbrahimiFard, Kurusch;
Schmeding, Alexander.
(2024)
Decompositions of nonlinear input–output systems to zero the output.
Systems & control letters (Print)
Academic article
2023

Celledoni, Elena;
Glöckner, Helge;
Riseth, Jørgen Nilsen;
Schmeding, Alexander.
(2023)
Deep neural networks on diffeomorphism groups for optimal shape reparametrization.
BIT Numerical Mathematics
Academic article

Schmeding, Alexander.
(2023)
On the unit component of the NewmanUnti group.
Classical and Quantum Gravity
Academic article

Maurelli, Mario;
Modin, Klas;
Schmeding, Alexander.
(2023)
Incompressible Euler equations with stochastic forcing: A geometric approach.
Stochastic Processes and their Applications
Academic article

Jensen, Mari Solberg;
Schmeding, Alexander.
(2023)
Jupyter notatbok i programmering.
Tangenten  Tidsskrift for matematikkundervisning
Article in business/trade/industry journal

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
Academic chapter/article/Conference paper

Gray, W. Steven;
EbrahimiFard, Kurusch;
Schmeding, Alexander.
(2023)
Zeroing the Output of Nonlinear Systems Without Relative Degree.
IEEE conference proceedings
Academic chapter/article/Conference paper
2022

Julien, Antoine Laurent Christophe;
Romijn, Elisabeth Inge;
Schmeding, Alexander.
(2022)
Peer and selfassessment to improve mathematics competence in preservice middleschool teachers.
European Society for Research in Mathematics Education
Academic chapter/article/Conference paper

Schmeding, Alexander.
(2022)
An Introduction to InfiniteDimensional Differential Geometry.
Cambridge University Press
Cambridge Studies in Advanced Mathematics
Academic monograph

Grong, Erlend;
Nilssen, Torstein;
Schmeding, Alexander.
(2022)
Geometric rough paths on infinite dimensional spaces.
Journal of Differential Equations
Academic article

Glöckner, Helge;
Schmeding, Alexander.
(2022)
Manifolds of mappings on Cartesian products.
Annals of Global Analysis and Geometry
Academic article

Gray, W. Steven;
Palmstrøm, Mathias;
Schmeding, Alexander.
(2022)
Continuity of Formal Power Series Products in Nonlinear Control Theory.
Foundations of Computational Mathematics
Academic article

Prinz, David Nicolas;
Schmeding, Alexander.
(2022)
Lie theory for asymptotic symmetries in general relativity: The NU group.
Classical and Quantum Gravity
Academic article

Prinz, David Nicolas;
Schmeding, Alexander.
(2022)
Lie theory for asymptotic symmetries in general relativity: The BMS Group.
Classical and Quantum Gravity
Academic article
2021

EbrahimiFard, 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)
Report

Roberts, David M.;
Schmeding, Alexander.
(2021)
Extending Whitney's extension theorem: nonlinear function spaces.
Annales de l'Institut Fourier
Academic article

Dahmen, Rafael;
Gray, W. Steven;
Schmeding, Alexander.
(2021)
Continuity of ChenFliess Series for Applications in System Identification and Machine Learning.
IFACPapersOnLine
Academic article

Schmeding, Alexander.
(2021)
Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application.
John Wiley & Sons
Academic chapter/article/Conference paper

Schmeding, Alexander.
(2021)
Applications of inﬁnitedimensional geometry and Lie theory
Habilitationsschrift.
Technische Universität Berlin
Doctoral dissertation
2020

Schmeding, Alexander;
Amiri, Habib;
Glöckner, Helge.
(2020)
Lie groupoids of mappings taking values in a Lie groupoid.
Archivum mathematicum
Academic article

Schmeding, Alexander;
Dahmen, Rafael.
(2020)
Lie groups of controlled characters of combinatorial Hopf algebras.
Annales de l’Institut Henri Poincaré D (AIHPD)
Academic article
2019

Schmeding, Alexander.
(2019)
The Lie group of vertical bisections of a regular Lie groupoid.
Forum mathematicum
Academic article

Curry, Charles Henry Alexander;
Schmeding, Alexander.
(2019)
Convergence of Lie group integrators.
Numerische Mathematik
Academic article

Amiri, Habib;
Schmeding, Alexander.
(2019)
A Differentiable Monoid of Smooth Maps on Lie Groupoids.
Journal of Lie theory
Academic article
2018

Celledoni, Elena;
Eidnes, Sølve;
Schmeding, Alexander.
(2018)
Shape analysis on homogeneous spaces: a generalised SRVT framework.
Abel Symposia
Academic article

Bogfjellmo, Geir;
Schmeding, Alexander.
(2018)
The geometry of characters of hopf algebras.
Abel Symposia
Academic article
2017

Bogfjellmo, Geir;
Schmeding, Alexander.
(2017)
The Lie Group Structure of the Butcher Group.
Foundations of Computational Mathematics
Academic article

Celledoni, Elena;
Eidnes, Sølve;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2017)
Shape analysis on lie groups and homogeneous spaces.
Lecture Notes in Computer Science (LNCS)
Academic article

Celledoni, Elena;
Eidnes, Sølve;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2017)
Shape analysis on Lie groups and homogeneous manifolds.
Proceedings of the GSI conference 2017
Abstract

Schmeding, Alexander;
Hjelle, Eivind Otto.
(2017)
Strong topologies for spaces of smooth maps with infinitedimensional target.
Expositiones mathematicae
Academic article
2016

Schmeding, Alexander;
Wockel, Christoph.
(2016)
(Re)constructing Lie groupoids from their bisections and applications to prequantisation.
Differential geometry and its applications
Academic article

Celledoni, Elena;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2016)
Shape analysis on Lie groups with application in computer animation.
Journal of Geometric Mechanics (JGM)
Academic article

Bogfjellmo, Geir;
Schmeding, Alexander.
(2016)
The tame Butcher group.
Journal of Lie theory
Academic article

Schmeding, Alexander;
Wockel, Christoph.
(2016)
Functorial aspects of the reconstruction of Lie groupoids from their bisections.
Journal of the Australian Mathematical Society
Academic article

Bogfjellmo, Geir;
Dahmen, Rafael;
Schmeding, Alexander.
(2016)
Character groups of Hopf algebras as infinitedimensional Lie groups.
Annales de l'Institut Fourier
Academic article
2015

Schmeding, Alexander.
(2015)
The diffeomorphism group of a noncompact orbifold.
Dissertationes Mathematicae
Academic article

Schmeding, Alexander;
Alzaareer, Hamza.
(2015)
Differentiable mappings on products with different degrees of differentiability in the two factors.
Expositiones mathematicae
Academic article

Dahmen, Rafael;
Schmeding, Alexander.
(2015)
The Lie group of real analytic diffeomorphisms is not real analytic.
Studia Mathematica
Academic article

Schmeding, Alexander;
Wockel, Christoph.
(2015)
The Lie group of bisections of a Lie groupoid.
Annals of Global Analysis and Geometry
Academic article
Journal publications

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
Academic article

Gray, W. Steven;
EbrahimiFard, Kurusch;
Schmeding, Alexander.
(2024)
Decompositions of nonlinear input–output systems to zero the output.
Systems & control letters (Print)
Academic article

Celledoni, Elena;
Glöckner, Helge;
Riseth, Jørgen Nilsen;
Schmeding, Alexander.
(2023)
Deep neural networks on diffeomorphism groups for optimal shape reparametrization.
BIT Numerical Mathematics
Academic article

Schmeding, Alexander.
(2023)
On the unit component of the NewmanUnti group.
Classical and Quantum Gravity
Academic article

Maurelli, Mario;
Modin, Klas;
Schmeding, Alexander.
(2023)
Incompressible Euler equations with stochastic forcing: A geometric approach.
Stochastic Processes and their Applications
Academic article

Jensen, Mari Solberg;
Schmeding, Alexander.
(2023)
Jupyter notatbok i programmering.
Tangenten  Tidsskrift for matematikkundervisning
Article in business/trade/industry journal

Grong, Erlend;
Nilssen, Torstein;
Schmeding, Alexander.
(2022)
Geometric rough paths on infinite dimensional spaces.
Journal of Differential Equations
Academic article

Glöckner, Helge;
Schmeding, Alexander.
(2022)
Manifolds of mappings on Cartesian products.
Annals of Global Analysis and Geometry
Academic article

Gray, W. Steven;
Palmstrøm, Mathias;
Schmeding, Alexander.
(2022)
Continuity of Formal Power Series Products in Nonlinear Control Theory.
Foundations of Computational Mathematics
Academic article

Prinz, David Nicolas;
Schmeding, Alexander.
(2022)
Lie theory for asymptotic symmetries in general relativity: The NU group.
Classical and Quantum Gravity
Academic article

Prinz, David Nicolas;
Schmeding, Alexander.
(2022)
Lie theory for asymptotic symmetries in general relativity: The BMS Group.
Classical and Quantum Gravity
Academic article

Roberts, David M.;
Schmeding, Alexander.
(2021)
Extending Whitney's extension theorem: nonlinear function spaces.
Annales de l'Institut Fourier
Academic article

Dahmen, Rafael;
Gray, W. Steven;
Schmeding, Alexander.
(2021)
Continuity of ChenFliess Series for Applications in System Identification and Machine Learning.
IFACPapersOnLine
Academic article

Schmeding, Alexander;
Amiri, Habib;
Glöckner, Helge.
(2020)
Lie groupoids of mappings taking values in a Lie groupoid.
Archivum mathematicum
Academic article

Schmeding, Alexander;
Dahmen, Rafael.
(2020)
Lie groups of controlled characters of combinatorial Hopf algebras.
Annales de l’Institut Henri Poincaré D (AIHPD)
Academic article

Schmeding, Alexander.
(2019)
The Lie group of vertical bisections of a regular Lie groupoid.
Forum mathematicum
Academic article

Curry, Charles Henry Alexander;
Schmeding, Alexander.
(2019)
Convergence of Lie group integrators.
Numerische Mathematik
Academic article

Amiri, Habib;
Schmeding, Alexander.
(2019)
A Differentiable Monoid of Smooth Maps on Lie Groupoids.
Journal of Lie theory
Academic article

Celledoni, Elena;
Eidnes, Sølve;
Schmeding, Alexander.
(2018)
Shape analysis on homogeneous spaces: a generalised SRVT framework.
Abel Symposia
Academic article

Bogfjellmo, Geir;
Schmeding, Alexander.
(2018)
The geometry of characters of hopf algebras.
Abel Symposia
Academic article

Bogfjellmo, Geir;
Schmeding, Alexander.
(2017)
The Lie Group Structure of the Butcher Group.
Foundations of Computational Mathematics
Academic article

Celledoni, Elena;
Eidnes, Sølve;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2017)
Shape analysis on lie groups and homogeneous spaces.
Lecture Notes in Computer Science (LNCS)
Academic article

Celledoni, Elena;
Eidnes, Sølve;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2017)
Shape analysis on Lie groups and homogeneous manifolds.
Proceedings of the GSI conference 2017
Abstract

Schmeding, Alexander;
Hjelle, Eivind Otto.
(2017)
Strong topologies for spaces of smooth maps with infinitedimensional target.
Expositiones mathematicae
Academic article

Schmeding, Alexander;
Wockel, Christoph.
(2016)
(Re)constructing Lie groupoids from their bisections and applications to prequantisation.
Differential geometry and its applications
Academic article

Celledoni, Elena;
Eslitzbichler, Markus;
Schmeding, Alexander.
(2016)
Shape analysis on Lie groups with application in computer animation.
Journal of Geometric Mechanics (JGM)
Academic article

Bogfjellmo, Geir;
Schmeding, Alexander.
(2016)
The tame Butcher group.
Journal of Lie theory
Academic article

Schmeding, Alexander;
Wockel, Christoph.
(2016)
Functorial aspects of the reconstruction of Lie groupoids from their bisections.
Journal of the Australian Mathematical Society
Academic article

Bogfjellmo, Geir;
Dahmen, Rafael;
Schmeding, Alexander.
(2016)
Character groups of Hopf algebras as infinitedimensional Lie groups.
Annales de l'Institut Fourier
Academic article

Schmeding, Alexander.
(2015)
The diffeomorphism group of a noncompact orbifold.
Dissertationes Mathematicae
Academic article

Schmeding, Alexander;
Alzaareer, Hamza.
(2015)
Differentiable mappings on products with different degrees of differentiability in the two factors.
Expositiones mathematicae
Academic article

Dahmen, Rafael;
Schmeding, Alexander.
(2015)
The Lie group of real analytic diffeomorphisms is not real analytic.
Studia Mathematica
Academic article

Schmeding, Alexander;
Wockel, Christoph.
(2015)
The Lie group of bisections of a Lie groupoid.
Annals of Global Analysis and Geometry
Academic article
Books

Schmeding, Alexander.
(2022)
An Introduction to InfiniteDimensional Differential Geometry.
Cambridge University Press
Cambridge Studies in Advanced Mathematics
Academic monograph
Part of book/report

Gray, W Steven;
Pham, Natalie;
Schmeding, Alexander.
(2024)
Distributional Generating Series in Nonlinear Control Theory.
IEEE conference proceedings
Academic chapter/article/Conference paper

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
Academic chapter/article/Conference paper

Gray, W. Steven;
EbrahimiFard, Kurusch;
Schmeding, Alexander.
(2023)
Zeroing the Output of Nonlinear Systems Without Relative Degree.
IEEE conference proceedings
Academic chapter/article/Conference paper

Julien, Antoine Laurent Christophe;
Romijn, Elisabeth Inge;
Schmeding, Alexander.
(2022)
Peer and selfassessment to improve mathematics competence in preservice middleschool teachers.
European Society for Research in Mathematics Education
Academic chapter/article/Conference paper

Schmeding, Alexander.
(2021)
Algebra is Geometry is Algebra – Interactions Between Hopf Algebras, Infinite Dimensional Geometry and Application.
John Wiley & Sons
Academic chapter/article/Conference paper
Report

EbrahimiFard, 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)
Report

Schmeding, Alexander.
(2021)
Applications of inﬁnitedimensional geometry and Lie theory
Habilitationsschrift.
Technische Universität Berlin
Doctoral dissertation
Teaching
Supervision
If you are a student interested in writing a thesis or a project under my supervision, please contact me. I keep a list of suitable problems for such projects connected to my research interests (check Research page).
Knowledge Transfer
2023

LectureSchmeding, Alexander. (2023) Publishing with master students. Nord universitet Faculty seminar  Matematikkseksjon , Bodø 20231130  20231130
2019

Academic lectureSchmeding, Alexander. (2019) A geometric view on stochastic Euler equations. Hausdorff Institute Bonn Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations , Bonn 20191111  20191115
2017

Academic lectureSchmeding, Alexander; Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus. (2017) Shape analysis on Lie groups and beyond. MekIT’17  9th National Conference on Computational Mechanics , NTNU Trondheim 20170511  20170512

Academic lectureSchmeding, Alexander. (2017) Infinitedimensional Lie groups for regularity structures of SPDEs. TU Berlin and Weierstraß Institut 7th Annual ERC BerlinOxford Young Researchers Meeting on Applied Stochastic Analysis , Weierstraß Institute Berlin, Tyskland 20170518  20170520
2016

Academic lectureCelledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Shape analysis on Lie groups with applications in computer animation. Universita' di Trieste SDIDE , Trieste 20160621  20160624

Academic lectureCelledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Lie groups shape analysis and computer animation. NTNU and UiB MaGIC , Ilsetra 20160218  20160221

Academic lectureCelledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Shape analysis on Lie groups with applications in computer animation. CeMEAI, ICMECC, SBMAC International Workshop on Industrial Mathematics , Campinas – Sao Paulo, Brazil 20160505  20160506

Academic lectureCelledoni, Elena; Eslitzbichler, Markus; Schmeding, Alexander. (2016) Shape analysis on Lie groups with applications in computer animation. MFO Oberwolfach Workshop , Oberwolfach 20160320  20160326

Academic lectureSchmeding, Alexander. (2016) Charakter Gruppen von HopfAlgebren als unendlichdimensionale Lie Gruppen. TU Dortmund 38. Nordwestdeutsches Funktionalanalysis Kolloquium , Dortmund 20160609  20160609

PosterSchmeding, Alexander; Celledoni, Elena; Eslitzbichler, Markus. (2016) Shape Analysis on Lie Groups (and beyond) with Applications. NTNU Trondheim Math meets Industry , Scandic Lerkendal Hotel, Trondheim 20160922  20160923
2015

LectureSchmeding, Alexander. (2015) Character groups of Hopf algebras as infinitedimensional Lie groups. Analysis group Bergen Differential Geometry, Geometric Invariants, and Vision Theory , University of Bergen, Bergen 20150423  20150425

LectureSchmeding, Alexander. (2015) Linking Lie Groupoids and InfiniteDimensional Lie Groups. KarlHermann Neeb (Erlangen) Lie Groups: Representations and Geometry; 49th "Seminar Sophus Lie" , Department Mathematik, Universität Erlangen 20150922  20150925

LectureSchmeding, Alexander. (2015) The Lie group of bisections of a Lie groupoid. Center for Mathematical Physics, Hamburg Infinitedimensional Structures in Higher Geometry and Representation Theory , Hamburg 20150216  20150220
2014

Academic lectureSchmeding, Alexander. (2014) Differential geometry on orbifolds: A smooth path through singularities. Research groups of C. Wockel, C. Schweigert and I. Runkel Seminar talk , Universität Hamburg 20140513 

Academic lectureSchmeding, Alexander. (2014) The Lie group of real analytic diffeomorphisms is not real analytic. Research group UnendlichDimensionale Analysis und Geometrie Seminar talk , Universität Paderborn 20140506 