Dr Matthias Langer
Senior Lecturer
Mathematics and Statistics
Personal statement
Personal statement
I am a 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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Canonical systems whose Weyl coefficients have dominating real part Langer Matthias, Pruckner Raphael, Woracek Harald Journal d'Analyse Mathématique (2023) https://doi.org/10.1007/s11854-023-0297-9 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 (2023) Discrete fragmentation equations with time-dependent coefficients Kerr Lyndsay, Lamb Wilson, Langer Matthias Discrete and Continuous Dynamical Systems - series S (2023) https://doi.org/10.3934/dcdss.2022211 Discrete fragmentation systems in weighted ℓ1 spaces Kerr Lyndsay, Lamb Wilson, Langer Matthias Journal of Evolution Equations Vol 20, pp. 1419-1451 (2020) https://doi.org/10.1007/s00028-020-00561-6 Spectral enclosures for a class of block operator matrices Giribet Juan, Langer Matthias, Martínez Pería Francisco, Philipp Friedrich, Trunk Carsten Journal of Functional Analysis Vol 278 (2020) https://doi.org/10.1016/j.jfa.2019.108455 Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice Estrada Ernesto, Hameed Ehsan Mejeed, Langer Matthias, Puchalska Aleksandra Linear Algebra and its Applications Vol 555, pp. 373-397 (2018) https://doi.org/10.1016/j.laa.2018.06.026
Publications
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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
Maths DTP 2020 University of Strathclyde | Fry, Mark Dolean Maini, Victorita (Principal Investigator) Langer, Matthias (Co-investigator) Fry, Mark (Research Co-investigator) 01-Jan-2021 - 01-Jan-2024 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 - 01-Jan-2024 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-2023 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
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
Projects
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Contact
Dr
Matthias
Langer
Senior Lecturer
Mathematics and Statistics
Email: m.langer@strath.ac.uk
Tel: 548 3821