Projects per year

## Personal profile

### 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/

### 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

## Fingerprint Dive into the research topics where Matthias Langer is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

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## Projects 2007 2022

## University of Strathclyde NPIF 2018 (NPIF EPSRC Doctoral) | Doherty, Michael

Waurick, M., Langer, M. & Doherty, M.

EPSRC (Engineering and Physical Sciences Research Council)

1/10/18 → 1/10/22

Project: Research Studentship - Internally Allocated › Research Studentship (Internally Allocated)

## Research Output 2000 2018

## Collimated dual species oven source and its characterisation via spatially resolved fluorescence spectroscopy

Cooper, N., Da Ros, E., Nute, J., Baldolini, D., Jouve, P., Hackermüller, L. & Langer, M., 14 Mar 2018, In : Journal of Physics D: Applied Physics. 51, 10, 8 p., 105602.Research output: Contribution to journal › Article

## Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Estrada, E., Hameed, E. M., Langer, M. & Puchalska, A., 15 Oct 2018, In : Linear Algebra and its Applications. 555, p. 373-397 25 p.Research output: Contribution to journal › Article

## Thesis

## Mathematical analysis of k-path Laplacian operators on simple graphs

Author: Hameed, E. M., 1 Nov 2017Supervisor: Langer, M. (Supervisor) & (Supervisor)

Student thesis: Doctoral Thesis

## Mathematical model based methods for characterising defects within ultrasonic non destructive evaluation

Author: Cunningham, L., 1 Aug 2014Supervisor: Mulholland, A. (Supervisor) & Langer, M. (Supervisor)

Student thesis: Doctoral Thesis

## Activities 2008 2016

## Quaestiones Mathematicae (Journal)

Matthias Langer (Editorial board member)Activity: Publication peer-review and editorial work types › Editorial board member

## Complex Analysis and Operator Theory (Journal)

Matthias Langer (Editorial board member)Activity: Publication peer-review and editorial work types › Editorial board member