Dr Matthias Langer
Senior Lecturer
Mathematics and Statistics
Personal statement
Personal statement
I am a senior lecturer in the Department of Mathematics and Statistics, and my research focuses on functional analysis, operator theory and differential equations. I am interested both in the theoretical aspects and their applications to problems in engineering and science, like non-destructive testing, liquid crystals, networks, quantum mechanics and others.
After having received a PhD from the Vienna University of Technology I did post-docs at the University of Leicester, the University of Bremen and the Vienna University of Technology. In 2004 I joined the University of Strathclyde. I was Visiting Professor at the Vienna University of Technology in 2013 and 2014. Three times I was a Visiting Fellow at the Isaac Newton Institute for Mathematical Sciences.
Webpage - http://personal.strath.ac.uk/m.langer/
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Publications
- Estimates for the Weyl coefficient of a two-dimensional canonical system
- Langer Matthias, Pruckner Raphael, Woracek Harald
- Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Vol 25, pp. 2259-2330 (2024)
- https://doi.org/10.2422/2036-2145.202106_015
- Discrete fragmentation equations with time-dependent coefficients
- Kerr Lyndsay, Lamb Wilson, Langer Matthias
- Discrete and Continuous Dynamical Systems - series S Vol 17, pp. 1947-1965 (2024)
- https://doi.org/10.3934/dcdss.2022211
- Canonical systems whose Weyl coefficients have dominating real part
- Langer Matthias, Pruckner Raphael, Woracek Harald
- Journal d'Analyse Mathématique Vol 152, pp. 361-400 (2024)
- https://doi.org/10.1007/s11854-023-0297-9
- The radial hedgehog solution in the Landau–de Gennes theory : effects of the bulk potentials
- McLauchlan Sophie, Han Yucen, Langer Matthias, Majumdar Apala
- Physica D: Nonlinear Phenomena Vol 459 (2024)
- https://doi.org/10.1016/j.physd.2023.134019
- Karamata's theorem for regularized Cauchy transforms
- Langer Matthias, Woracek Harald
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics , pp. 1-61 (2024)
- https://doi.org/10.1017/prm.2023.128
- Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints
- Langer Matthias, Woracek Harald
- Function Spaces, Theory and Applications (2023) (2023)
- https://doi.org/10.1007/978-3-031-39270-2_5
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Research Interests
- differential operators, in particular elliptic PDOs and differential operators with singular coefficients
- functions whose values are operators on a Banach space for the study of spectral problems that depend nonlinearly on the eigenvalue parameter
- block operator matrices, i.e. matrices whose entries are operators between Banach spaces, with applications to systems of differential equations
- inverse problems: in particular, mathematical models for non-destructive testing with ultrasonic waves, inverse spectral problems for differential equations with singular coefficients
- operator semigroups and evolution equations, in particular, coagulation-fragmentation equations
- spaces with indefinite inner products and their use in singular perturbations and inverse spectral theory
Professional Activities
- Quaestiones Mathematicae (Journal)
- Editorial board member
- 2016
- Complex Analysis and Operator Theory (Journal)
- Editorial board member
- 2/2014
- Technical University of Berlin
- Visiting researcher
- 7/2010
- IWOTA 2010
- Keynote/plenary speaker
- 2010
- 25th Nordic and 1st British-Nordic Congress of Mathematicians
- Organiser
- 6/2009
- International Conference on Engineering and Computational Mathematics
- Invited speaker
- 2009
Projects
- Maths DTP 2020 University of Strathclyde | Fry, Mark
- Langer, Matthias (Principal Investigator) Dolean Maini, Victorita (Co-investigator) Fry, Mark (Research Co-investigator)
- 01-Jan-2021 - 01-Jan-2025
- Maths DTP 2020 University of Strathclyde | McLauchlan, Sophie
- Majumdar, Apala (Principal Investigator) Langer, Matthias (Co-investigator) McLauchlan, Sophie (Research Co-investigator)
- Ferronematics in Confinement - Modelling, Analysis and Simulations for New Applications; Value: 87,500.00 GBP
- 01-Jan-2020 - 06-Jan-2025
- University of Strathclyde NPIF 2018 (NPIF EPSRC Doctoral) | Doherty, Michael
- Langer, Matthias (Principal Investigator) Waurick, Marcus (Co-investigator) Doherty, Michael (Research Co-investigator)
- 01-Jan-2018 - 01-Jan-2024
- Doctoral Training Partnership (DTP - University of Strathclyde) | Ross, Grant Jamieson
- Langer, Matthias (Principal Investigator) Estrada, Ernesto (Co-investigator) Ross, Grant Jamieson (Research Co-investigator)
- 01-Jan-2015 - 01-Jan-2019
- Spectral Theory of Block Operator Matrices
- Langer, Matthias (Principal Investigator)
- Block operator matrices are matrices whose entries are operators in Hilbert or Banach spaces. Such operators appear in a natural way when systems of differential equations with different order and type are investigated or an operator in a given space is considered that has a natural decomposition intosubspaces. In many applications of mathematical physics it is natural and fruitful to use the theory of block operator matrices. It is the aim to study spectral properties of such block operator matrices: location of the essential spectrum, variational principles and estimates for eigenvalues, investigation of spectral subspaces, basis properties of components of eigenvectors and generalised Fourier transforms. Particular emphasis is placed on unbounded block operator matrices, for which different cases have to be considered separately; these cases depend on the places where the strongest operators are located. The results should be applied to concrete operators arising in applications, mainly ordinary or partial differential operators.
- 01-Jan-2007 - 30-Jan-2009
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Contact
Dr
Matthias
Langer
Senior Lecturer
Mathematics and Statistics
Email: m.langer@strath.ac.uk
Tel: 548 3821