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Karl Schmidt

Professor Karl Schmidt

Professor

School of Mathematics

Email
SchmidtKM@cardiff.ac.uk
Telephone
+44 29208 76778
Campuses
Abacws, Room 2.18, Senghennydd Road, Cathays, Cardiff, CF24 4AG

Overview

My research interests include Ordinary and Partial Differential Operators, Spectral Theory and Mathematical Physics, Asymptotic Analysis of Differential Equations, Additive Combinatorics and Number Theory, Linear Algebra, and Mathematical Methods in Medical Genetics.

Administrative functions

Director of Postgraduate Research Studies

Publication

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1995

1993

Articles

Book sections

Books

  • Brown, B. M., Eastham, M. S. P. and Schmidt, K. M. 2013. Periodic differential operators. Operator Theory: Advances and Applications Vol. 230. Basel: Birkhäuser.

Conferences

  • Schmidt, K. M. and Umeda, T. 2014. Spectral properties of massless Dirac operators with real-valued potentials. Presented at: Spectral and scattering theory and related topics, Kyoto University, Japan, 14-16 December 2011RIMS Kôkyûroku Bessatsu B45: Spectral and Scattering Theory and Related Topics. Kyoto, Japan: pp. 25-30.
  • Brown, B. M., Langer, M. and Schmidt, K. M. 2008. The HELP inequality on trees. Presented at: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8 January - 29 June 2007 Presented at Exner, P. et al. eds.Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society pp. 337-354.

Research

Research interests

  • Spectral Theory, Differential Operators and Mathematical Physics
  • Asymptotic Analysis of Differential Equations
  • Linear Algebra, Additive Combinatorics
  • Analysis in Probability Theory
  • Mathematical Methods in Medical Genetics

Research group

Teaching

Undergraduate - Spring semester

  • MA1001 Elementary Differential Equations / MA1051 Hafaliadau Differol Elfennol
  • MA3005 Functional and Fourier Analysis

Postgraduate - Autumn semester

  • MAGIC057 Spectral Theory of Ordinary Differential Operators

Biography

Qualifications

  • 1990 Dipl. phys. (Ludwig-Maximilians-Universität München)
  • 1992 Dr. rer. nat. (Ludwig-Maximilians-Universität München)
  • 1999 Habilitation (Ludwig-Maximilians-Universität München)

Previous academic positions

  • 1992-1993 Research fellow (Mathematisches Institut, LMU München)
  • 1993-2000 Lecturer (Mathematisches Institut, LMU München)
  • 1994-1995 Visiting Associate (Dept Mathematics, California Institute of Technology, Pasadena)
  • 2000-2003 Lecturer (School of Mathematics, Cardiff)
  • 2003-2009 Senior Lecturer (School of Mathematics, Cardiff)
  • 2009-2017 Reader (School of Mathematics, Cardiff)

Honours

  • 2020 Elected Fellow of the Learned Society of Wales

Supervisions

Postgraduate students

Current

    • A Law (joint supervision with M C Lettington) - Additive Combinatorics
    • G S Jameel - Spectral Theory

Graduated

  • S Monaquel (joint supervision with W D Evans) - Some Problems Associated with Differential and Difference Equations, PhD 2004
  • S Aumann (joint supervision with B M Brown) - A Hardy-Littlewood-Type Inequality for the p-Laplacian, MPhil 2007
  • M Ghodsi (joint supervision with V Moskvina) - Analysis of Dynamical Processes for Test Assessment in Medical Genetics, PhD 2012
  • D Hughes - Spectral Analysis of Dirac Operators under Integrability Conditions, PhD 2012
  • M Vronskaya (joint supervision with A Zhigljavsky) - Stability of Singular Spectrum Analysis and Causality in Time Series, Phd 2014
  • S Hill (joint supervision with M Lettington) - Problems Related to Number Theory: Sum-and-Distance Systems, Reversible Squares Matrices and Divisor Functions, PhD 2018
  • E Baker (jointly with V Escott-Price (main supervisor) et al, MEDIC) - Investigation of New Strategies for Identifying Causal Mechanisms in Alzheimer's Disease Taking Bioinformatics Approaches Beyond GWAS, PhD 2018
  • T Phillips (joint supervision with A Zhigljavsky) - On Positive and Conditionally Negative Definite Functions with a Singularity at Zero, and their Applications in Potential Theory, PhD 2018
  • M Lewis (joint supervision with K Cherednichenko, Bath) - Stability of Solutions of a One-dimensional p-Laplace Equation with Periodic Potential, PhD 2019