Dr Matthias Langer


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/



Quasi boundary triples and semibounded self-adjoint extensions
Behrndt Jussi, Langer Matthias, Lotoreichik Vladimir, Rohleder Jonathan
Proceedings of the Royal Society of Edinburgh: Section A Mathematics Vol 147, pp. 895-916 (2017)
Trace formulae for Schrödinger operators with singular interactions
Behrndt Jussi, Langer Matthias, Lotoreichik Vladimir
Functional Analysis and Operator Theory for Quantum Physics (2017) (2017)
Spectral properties of unbounded J-self-adjoint block operator matrices
Langer Matthias, Strauss Michael
Journal of Spectral Theory Vol 7, pp. 137-190 (2017)
Variational principles for self-adjoint operator functions arising from second order systems
Jacob Birgit, Langer Matthias, Trunk Carsten
Operators and Matrices Vol 10, pp. 501-531 (2016)
Boundary triples for Schrödinger operators with singular interactions on hypersurfaces
Behrndt J, Langer M, Lotoreichik V
Nanosystems: Physics, Chemistry, Mathematics Vol 7, pp. 290-302 (2016)
Triple variational principles for self-adjoint operator functions
Langer Matthias, Strauss Michael
Journal of Functional Analysis Vol 270, pp. 2019-2047 (2016)

more publications

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


University of Strathclyde NPIF 2018 (NPIF EPSRC Doctoral) | Doherty, Michael
Waurick, Marcus (Principal Investigator) Langer, Matthias (Co-investigator) Doherty, Michael (Research Co-investigator)
01-Jan-2018 - 01-Jan-2022
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
New Methods For Ultrasonic NDE Of Difficult Materials | Tant, Katherine Margaret Mary
Mulholland, Anthony (Principal Investigator) Langer, Matthias (Co-investigator) Tant, Katherine Margaret Mary (Research Co-investigator)
01-Jan-2011 - 11-Jan-2014
Doctoral Training Grant 2010 | Cunningham, Laura
Mulholland, Anthony (Principal Investigator) Langer, Matthias (Co-investigator) Cunningham, Laura (Research Co-investigator)
01-Jan-2011 - 06-Jan-2015
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


Mathematics and Statistics
Livingstone Tower

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