###### Profiles

# Professor Alex Belton

### Head of School and substantive Professor of Mathematics

### School of Engineering, Computing and Mathematics (Faculty of Science and Engineering)

## Biography

Biography

Alexander Belton joined the University of Plymouth in September 2022 after 15 years with Lancaster University. At Lancaster he held a number of senior roles within the Department of Mathematics and Statistics, including five years as Head of Department. Prior to his time at Lancaster he held postdoctoral research positions at University College Cork, Université Claude Bernard Lyon 1 and Université Louis Pasteur Strasbourg 1.

Professor Belton was a key figure in the establishment of the Lancaster University School of Mathematics and is a trustee of its governing trust.

### Qualifications

- DPhil, University of Oxford
- MASt (Part III) Pure Mathematics, University of Cambridge
- BSc (Hons) Mathematics, University of Nottingham

### Professional membership

- Senior Fellow, Higher Education Academy
- Fellow, Institute for Mathematics and its Applications
- Member, London Mathematical Society
- Fellow, Royal Statistical Society
- Chartered Mathematician
- Chartered Scientist
- Member, American Mathematical Society
- Member, Irish Mathematical Society

### Roles on external bodies

- Member, EPSRC Peer Review College
- Member, Personnel Committee, London Mathematical Society
- Trustee, Rigby Education Trust

## Teaching

Teaching

### Staff serving as external examiners

- Bangor University International College (2018-22)
- Manchester Metropolitan University (2021-25)
- University College Cork (2022-25)
- University Kebangsaan Malaysia (2021-23)

## Research

Research

### Research interests

- Quantum probability
- Open quantum systems
- Operator semigroups
- Matrix positivity

### Research degrees awarded to supervised students

PhD students

- Michał Gnacik (2014)
- Jason Hancox (2018)

## Publications

Publications

Key publications

Key publications are highlighted

Journals
Articles

(2021) 'Moment-sequence transforms' Journal of the European Mathematical Society 24, (9) 3109-3160 , DOI

(2019) 'Simultaneous kernels of matrix Hadamard powers' Linear Algebra and its Applications 576, 142-157 , DOI

(2019) 'Quasifree Stochastic Cocycles and Quantum Random Walks' Journal of Statistical Physics 176, (1) 1-39 , DOI

(2018) 'Strong Convergence of Quantum Random Walks Via Semigroup Decomposition' Annales Henri Poincaré 19, (6) 1711-1746 , DOI

(2017) 'The cocycle identity holds under Stopping' The Quarterly Journal of Mathematics 68, (3) 817-830 , DOI

(2016) 'Matrix positivity preservers in fixed dimension. I' Advances in Mathematics 298, 325-368 , DOI

(2016) 'Matrix positivity preservers in fixed dimension' Comptes Rendus Mathematique 354, (2) 143-148 , DOI

(2015) 'An algebraic construction of quantum flows with unbounded generators' Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, (1) , DOI

(2014) 'Quantum Random Walks with General Particle States' Communications in Mathematical Physics 328, (2) 573-596 , DOI

(2014) 'STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES' The Quarterly Journal of Mathematics 65, (4) 1145-1164 , DOI

(2013) 'Quantum Feynman-Kac perturbations' Journal of the London Mathematical Society 89, (1) 275-300 , DOI

(2010) 'Quantum Random Walks and Thermalisation' Communications in Mathematical Physics 300, (2) 317-329 , DOI

(2010) 'Random-walk approximation to vacuum cocycles' Journal of the London Mathematical Society 81, (2) 412-434 , DOI

(2008) 'On the path structure of a semimartingale arising from monotone probability theory' Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 44, (2) , DOI

(2007) 'The chaotic-representation property for a class of normal martingales' Probability Theory and Related Fields 139, (3-4) 543-562 , DOI

(2006) 'SOME SELF-ADJOINT QUANTUM SEMIMARTINGALES' Proceedings of the London Mathematical Society 92, (3) 791-816 , DOI

(2004) 'An Isomorphism of Quantum Semimartingale Algebras' The Quarterly Journal of Mathematics 55, (2) 135-165 , DOI

(2001) 'Quantum Ω-Semimartingales and Stochastic Evolutions' Journal of Functional Analysis 187, (1) 94-109 , DOI

Chapters

(2019) 'A Panorama of Positivity. I: Dimension Free' Trends in Mathematics Springer International Publishing 117-165 , DOI

(2019) 'Introduction to Classical and Quantum Markov Semigroups' Open Quantum Systems Springer International Publishing 1-54 , DOI

Conference Papers

(2016) 'Schur polynomials and matrix positivity preservers' 155-166

(2007) 'ALICKI–FANNES AND HUDSON–PARTHASARATHY EVOLUTION EQUATIONS' Proceedings of the 26th Conference WORLD SCIENTIFIC , DOI

## Personal

Personal

### Conferences organised

- Co-organiser (with Dominique Guillot), mini-symposium on Matrix positivity: theory and applications, 2022 Meeting of the International Linear Algebra Society, National University of Ireland Galway (2022)

- Co-organiser (with Emilio Porcu and Mihai Putinar), workshop on Applied Matrix Positivity, International Centre for Mathematical Sciences, Edinburgh (2021)

### Other academic activities

- Editor,
*Infinite Dimensional Analysis, Quantum Probability and Related Topics*