Professor Marco Marletta
Overview
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Position:
Professor
Email:
marlettam@cardiff.ac.ukTelephone: +44(0)29 208 75552
Fax: +44(0)29 208 74199
Extension: 75552
Location: M/2.48
Research Interests
My interests are in spectral problems for ordinary and partial differential operators and involves both analysis and computational mathematics. The Engineering and Physical Sciences Research Council have funded my work since 1994 and I have also had significant funding from the Leverhulme Trust and the London Mathematical Society.
My most recent work has been on the numerical solution of spectral problems for ODEs and PDEs on infinite domains. Central to this has been the study of the Titchmarsh-Weyl function for the ODE case, and of the Dirichlet to Neumann map for the PDE case.
I also work on inverse problems in spectral theory: these involve determining a problem from a knowledge of its spectral properties, usually through the Dirichlet to Neumann map, and have numerous applications.
Please see my personal web page for further details.
Research Group
Analysis and Differential Equations
Recent Significant Publications
Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics, with B.M. Brown, C. Tretter, M. Langer and M. Wagenhofer (2010).
On the inverse resonance problem for Schrodinger operators, with R. Shterenberg and R. Weikard, to appear in Comm. Math. Phys. (under a slightly different title!).
Neumann–Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum (single author paper, 2009).
Analysis of Regge poles for the Schrodinger equation, with B.M. Brown and A. Hiscox (2009).
A Laplace operator with boundary conditions singular at one point, with Grigori Rozenblum (2009).
Teaching
Administrative Duties
Member of the School of Mathematics Management Board
Member of School Research Committee
Member of School Learning and Teaching Committee
Member of the Postgraduate Executive Team
Personal Website
Publications
Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics, with B.M. Brown, C. Tretter, M. Langer and M. Wagenhofer (2010).
On the inverse resonance problem for Schrodinger operators, with R. Shterenberg and R. Weikard, to appear in Comm. Math. Phys. (under a slightly different title!).
Neumann–Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum (single author paper, 2009).
Analysis of Regge poles for the Schrodinger equation, with B.M. Brown and A. Hiscox (2009).
A Laplace operator with boundary conditions singular at one point, with Grigori Rozenblum (2009).
The abstract Titchmarsh-Weyl $M$-function for adjoint operator pairs and its relation to the spectrum, with B.M. Brown, J. Hinchcliffe, S. Naboko and I. Wood (2009).
A simple method of calculating eigenvalues and resonances in domains with infinite regular ends, with Michael Levitin (2008).
Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices, with B.M. Brown, S. Naboko and I. Wood (2008).
Essential spectra of coupled systems of differential equations and applications in hydrodynamics, with Ch. Tretter (2007).
Absence of the absolutely continuous spectrum of a first-order non-selfadjoint Dirac-like system with slowly decaying perturbations, with R. Romanov (2006).
Numerical computation of eigenvalues in the spectral gaps of Sturm-Liouville operators, with L.Aceto and P. Ghelardoni (2006).
Weak stability for an inverse Sturm-Liouville problem with finite spectral data and complex potential, with R. Weikard (2005).
Floquet theory for left-definite Sturm-Liouville problems, with A. Zettl (2005).
Spectral concentrations and resonances of a second-order block operator matrix and an associated $\lambda$-rational Sturm-Liouville problem, with B.M. Brown and M. Langer (2004).
Eigenvalue problems on exterior domains and Dirichlet to Neumann maps (2004).
The Ekman flow and related problems: spectral theory and numerical analysis, with L. Greenberg (2004).
Spectral inclusion and spectral exactness for PDEs on exterior domains, with B.M. Brown (2004).
Eigenvalue bounds for the singular Sturm-Liouville problem with a complex potential, with B.M. Brown, M. Langer, C. Tretter and M. Wagenhofer (2003).
Numerical solution of a $\lambda$-rational Sturm-Liouville problem, with P. Ghelardoni and G. Gheri (2003).
Counting and computing eigenvalues of left-definite Sturm-Liouville problems , with A. Zettl (2002).
Numerical solution of non-self-adjoint Sturm-Liouville problems and related systems, with L. Greenberg (2001).
Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems, with B.M. Brown (2001).
The Friedrichs extension of singular differential operators, with A. Zettl (2000).
Research
Current and Past Collaborators
Malcolm Brown in the Computer Science Department here in Cardiff.
Des Evans in the School of Mathematics here in Cardiff.
Paolo Ghelardoni and Giovanni Gheri at Universita` di Pisa.
Leon Greenberg at the University of Maryland at College Park, sadly deceased in September 2003. James Hinchcliffe here in Cardiff.
Lucas Jodar of Universitat Politecnica de Valencia.
Ian Knowles of University of Alabama at Birmingham.
Michael Levitin here in Cardiff, the new WIMCS professor of analysis.
Carsten Maple, now at Luton. Carsten was my first PhD student and got a chair before I did.
Sergei Naboko of Saint Petersburg State University.
John Pryce of the Royal Military College of Science, who was my PhD supervisor.
Roman Romanov of Saint Petersburg State University.
Andrei Shkalikov of Moscow State University.
Christiane Tretter of the University of Bern.
Matthias Langer of the University of Strathclyde
Marcus Wagenhofer of the University of Bremen.
Anton Zettl of Northern Illinois University.
Rudi Weikard of University of Alabama at Birmingham.
Ian Wood in Aberystwyth.
External Funding Since 2000
EPSRC postdoc grant GR/R20885/01 (2002 to 2005)
EPSRC postdoc grant EP/C008324/1 (2006 to 2008)
EPSRC VF grant GR/S74072/01 (2004 to 2006)
EPSRC VF grant GR/S47229/01 (2004)
Leverhulme Fellowship (2001 to 2002)
EPSRC VF grant GR/R44959/01 (2001 to 2002)
EPSRC VF grant GR/N26159/01 (2000 to 2001)
I have also had LMS funding for a number of short meetings.
Invited Conference and Workshop Talks
Bath-RAL NA Day, September 2008
`Numerical Approaches to Oscillatory Functions', Ghent, January 2008.
Banach Centre Spectral Theory Workshop, Warsaw, 2007; 2005; 2003.
Inverse Problems Workshop, Liverpool, 2006.
Durham Symposium on Spectral Theory, 2005
Operator Theory and Applications in Mathematical Physics', keynote speaker, Poland, 2004.
AMS Meeting, Nashville, 2004.
Scottish Computational Mathematics Symposium, Edinburgh, 2001.
Postgraduate Students
Current Research Students
Aaron Hiscox (PhD student)
Ahmed Muhammad (PhD student)
Previous
Vic Duoba (Mphil student)
Carsten Maple (PhD student, now a professor of Computer Science)
Kieran Robert (PhD student)