Dr Matthias Langer

Senior Lecturer

Mathematics and Statistics


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/


Back to staff profile

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
Complex Analysis and Operator Theory (Journal)
Editorial board member
Technical University of Berlin
Visiting researcher
IWOTA 2010
Keynote/plenary speaker
25th Nordic and 1st British-Nordic Congress of Mathematicians
International Conference on Engineering and Computational Mathematics
Invited speaker

More professional activities


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 - 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-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

More projects

Back to staff profile


Dr Matthias Langer
Senior Lecturer
Mathematics and Statistics

Email: m.langer@strath.ac.uk
Tel: 548 3821