# Professor Marco Marletta

Deputy Head of School

- marlettam@cardiff.ac.uk
- +44 (0)29 2087 5552
- M/2.41, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

## Overview

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

### Administrative duties

- Director of Research
- 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

## Biography

## Publications

### 2021

- Aljawi, S. and Marletta, M. 2021. On the eigenvalues of spectral gaps of matrix-valued Schrödinger operators. Numerical Algorithms 86, pp. 637-657. (10.1007/s11075-020-00904-x)
- Ben-Artzi, J., Marletta, M. and Rosler, F. 2021. Computing the sound of the sea in a seashell. Foundations of Computational Mathematics

### 2020

- Bogli, S. and Marletta, M. 2020. Essential numerical ranges for linear operator pencils. IMA Journal of Numerical Analysis 40(4), pp. 2256-2308. (10.1093/imanum/drz049)
- Bogli, S., Marletta, M. and Tretter, C. 2020. The essential numerical range for unbounded linear operators. Journal of Functional Analysis 279(1), article number: 108509. (10.1016/j.jfa.2020.108509)
- Brown, B. M.et al. 2020. The functional model for maximal dissipative operators (translation form): an approach in the spirit of operator knots. Transactions of the American Mathematical Society 373, pp. 4145-4187. (10.1090/tran/8029)

### 2019

- Brown, B. M.et al. 2019. The detectable subspace for the Friedrichs model. Integral Equations and Operator Theory 91, article number: 49. (10.1007/s00020-019-2548-9)
- Alberti, G. S.et al. 2019. Essential spectrum for Maxwell's equations. Annales Henri Poincaré 20, pp. 1471-1499. (10.1007/s00023-019-00762-x)

### 2017

- Drabek, P., Kuliev, K. and Marletta, M. 2017. Some criteria for discreteness of spectrum of half-linear fourth order Sturm-Liouville problem. Nonlinear Differential Equations and Applications NoDEA 24(2), article number: 11. (10.1007/s00030-017-0433-2)
- Brown, B. M.et al. 2017. Inverse problems for boundary triples with applications. Studia Mathematica 237(3), pp. 241-275. (10.4064/sm8613-11-2016)

### 2016

- Brown, M., Marletta, M. and Symons, F. 2016. Uniqueness from discrete data in an inverse spectral problem for a pencil of ordinary differential operators. Journal of the London Mathematical Society 94(3), pp. 793-813. (10.1112/jlms/jdw059)
- Brown, B. M.et al. 2016. Detectable subspaces and inverse problems for Hain-Lüst-type operators. Mathematische Nachrichten 289(17-18), pp. 2108-2132. (10.1002/mana.201500231)
- Brown, B. M., Marletta, M. and Reyes Gonzales, J. M. 2016. Uniqueness for an inverse problem in electromagnetism with partial data. Journal of Differential Equations 260(8), pp. 6525-6547. (10.1016/j.jde.2016.01.002)

### 2014

- Boegli, S.et al. 2014. Guaranteed resonance enclosures and exclosures for atoms and molecules. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470(2171), article number: 20140488. (10.1098/rspa.2014.0488)
- Marletta, M. and Naboko, S. 2014. The finite section method for dissipative operators. Mathematika 60(2), pp. 415-443. (10.1112/S0025579314000126)

### 2013

- Marletta, M. and Tretter, C. 2013. Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow. Journal of Functional Analysis 264(9), pp. 2136-2176. (10.1016/j.jfa.2013.02.008)

### 2012

- Boulton, L., Marletta, M. and Rule, D. 2012. On the Stability of a Forward-Backward Heat Equation. Integral Equations and Operator Theory 73(2), pp. 195-216. (10.1007/s00020-012-1963-y)
- Marletta, M. and Scheichl, R. 2012. Eigenvalues in spectral gaps of differential operators. Journal of Spectral Theory 2(3), pp. 293-320. (10.4171/JST/30)

### 2010

- Marletta, M. 2010. Neumann-Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum. IMA Journal of Numerical Analysis 30(4), pp. 917-939. (10.1093/imanum/drp017)
- Hiscox, A. J., Brown, B. M. and Marletta, M. 2010. On the low energy behavior of Regge poles. Journal of Mathematical Physics 51(10), article number: 102104. (10.1063/1.3496811)
- Marletta, M., Shterenberg, R. and Weikard, R. 2010. On the inverse resonance problem for Schrödinger operators. Communications in Mathematical Physics 295(2), pp. 465-484. (10.1007/s00220-009-0928-8)
- Brown, B. M.et al. 2010. Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics. LMS Journal of Computation and Mathematics 13, pp. 65-81. (10.1112/S1461157008000466)

### 2009

- Marletta, M. and Rozenblum, G. 2009. A Laplace operator with boundary conditions singular at one point. Journal of Physics A: Mathematical and Theoretical 42(12), article number: 125204. (10.1088/1751-8113/42/12/125204)

### 2008

- Brown, B. M.et al. 2008. Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices. Journal of the London Mathematical Society 77(3), pp. 700-718. (10.1112/jlms/jdn006)

### 2007

- Marletta, M. and Tretter, C. 2007. Essential spectra of coupled systems of differential equations and applications in hydrodynamics. Journal of Differential Equations 243(1), pp. 36-69. (10.1016/j.jde.2007.09.002)

### 2005

- Marletta, M. and Weikard, R. 2005. Weak stability for an inverse Sturm-Liouville problem with finite spectral data and complex potential. Inverse problems 21(4), pp. 1275-1290. (10.1088/0266-5611/21/4/005)

### 2004

- Greenberg, L. and Marletta, M. 2004. The Ekman flow and related problems: spectral theory and numerical analysis. Mathematical Proceedings of the Cambridge Philosophical Society 136(3), pp. 719-764. (10.1017/S030500410300731X)
- Brown, B. M. and Marletta, M. 2004. Spectral inclusion and spectral exactness for PDEs on exterior domains. IMA Journal of Numerical Analysis 24(1), pp. 21-43. (10.1093/imanum/24.1.21)

### 2001

- Brown, B. M. and Marletta, M. 2001. Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 457(2005), pp. 117-139. (10.1098/rspa.2000.0659)

## Teaching

### Autumn semester

- Foundations tutorials

### Spring semester

- MA1001 Elementary Differential Equations
- MA3000 Complex Function Theory

### 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 a trustee of the charity DEBRA.
- Lucas Jodar of Universitat Politecnica de Valencia.
- Ian Knowles of University of Alabama at Birmingham.
- Michael Levitin of University of Reading.
- 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 School of Mathematics here in Cardiff, 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 formerly 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

I have obtained a number of grants, both as sole and as joint investigator. My research funding from EPSRC has been continuous since I obtained my first grant in 1994.

These figures do not include some small Royal Society grants or the £22K budget for the program on Pseudospectra at ICMS in Edinburg in September 2014.

EPSRC CTA grant income: £189,600 The CTA grant was to fund an MSc in Cardiff, proposed by myself, by B.M. Brown (Computer Science) and P.J. Knowles (Chemistry).

- Joint Investigator, EPSRC PDRA Grant on Inverse Problems in Magnetic Imaging: £430,833
- Principal Investigator, WIMCS-Leverhulme Fellowships on Dissipative Operator Theory (£160,977)
- Scientist in Charge, EU Marie Curie Project GRAPH-COUPL
- Principal Investigator, EPSRC PDRA grant, with B.M. Brown (2005)
- Sole applicant, EPSRC VF grant for Prof. C. Tretter (2004)
- Joint investigator, EPSRC VF grant for Prof. S.N. Naboko (2004)
- Leverhulme Fellowship (2001-2002)
- Principal investigator, EPSRC VF grant for Prof A.A. Shkalikov (2001)
- Sole applicant, EPSRC VF grant for Prof. L. Greenberg (2000)
- Sole applicant, EPSRC VF grant for Prof. L. J`odar (1998)
- Sole applicant, EPSRC VF grant for Prof. L. Greenberg (1998)
- Sole applicant, EPSRC VF grant for Prof. L. Greenberg (1996)
- Sole applicant, EPSRC VF grant for Prof. L. Greenberg (1994)
- Joint applicant, 1998 EPSRC Numerical Analysis Summer School
- Joint applicant, 1996 EPSRC Numerical Analysis Summer School
- Joint applicant, 1994 EPSRC Numerical Analysis Summer School
- Joint investigator, EPSRC PDRA grant, with B.M. Brown and W.D. Evans (2002)
- 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

Apart from the large meetings listed previously, I have been invited to speak at numerous other meetings. The list below includes only those for which my expenses were paid in full.

- AIM Workshop on the Mathematical Aspects of Physics with Nonselfadjoint Operators, June 2015.
- Plenary speaker, Kent Spectral Theory Meeting, Canterbury, March 2014.
- Plenary speaker, TU-Hamburg ‘Kickoff Meeting’ on Applied Analysis, Hamburg-Harburg, July 2012.
- Bath-RAL NA Conference, September 2008.
- `Numerical Approaches to Oscillatory Functions', Ghent, January 2008.
- Banach Centre Spectral Theory Workshop, Warsaw, 2007; 2005; 2003.
- Inverse Problems Workshop, University of Liverpool, March 2006.
- Durham Symposium on Spectral Theory, 2005
- Banach Centre Conference on Operator Theory, Warsaw, Poland, July 2005.
- American Mathematical Society Meeting, Nashville, Tenessee, October 2004.
- AMS Meeting, Nashville, 2004.
- Operator Theory and Applications in Mathematical Physics', keynote speaker, Poland, 2004.
- EPSRC Spectral Theory Network, December 2003.
- Banach Centre Conference on Operator Theory, Warsaw, Poland, August 2003.
- EPSRC Spectral Theory Network, October 2001.
- Scottish Computational Mathematics Symposium, Edinburgh, 2001.
- Interdisciplinary Research Conference, Universitat Politecnica de Valencia, September 2001. Organizer: L. J`odar.
- Scottish Computational Mathematics Conference, September 2001. Organizer: D. Sloan.
- ‘Geometric Integration’: EPSRC-LMS workshop, Durham, July 2000.
- Course of seminars on Hamiltonian Systems at the University of Pisa, April 1999.
- ‘Computational Spectral Theory’: EPSRC workshop (1996).
- ‘Computational Spectral Theory’: EPSRC workshop (1993).