Professor Alex Belton
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
  • MAdSt (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
Belton A, Guillot D, Khare A & Putinar M (2022) 'Hirschman–Widder densities' Applied and Computational Harmonic Analysis 60, 396-425 , DOI
Belton A, Guillot D, Khare A & Putinar M (2021) 'Moment-sequence transforms' Journal of the European Mathematical Society 24, (9) 3109-3160 , DOI
Belton A, Guillot D, Khare A & Putinar M (2020) 'A panorama of positivity. II: Fixed dimension' 109-150 , DOI
Belton A, Guillot D, Khare A & Putinar M (2019) 'Simultaneous kernels of matrix Hadamard powers' Linear Algebra and its Applications 576, 142-157 , DOI
Belton ACR, Gnacik M, Lindsay JM & Zhong P (2019) 'Quasifree Stochastic Cocycles and Quantum Random Walks' Journal of Statistical Physics 176, (1) 1-39 , DOI
Belton ACR (2018) 'On Stopping Fock-Space Processes' Journal of Theoretical Probability 32, (1) 484-526 , DOI
Belton ACR, Gnacik M & Lindsay JM (2018) 'Strong Convergence of Quantum Random Walks Via Semigroup Decomposition' Annales Henri Poincaré 19, (6) 1711-1746 , DOI
Belton ACR & Sinha KB (2017) 'The cocycle identity holds under Stopping' The Quarterly Journal of Mathematics 68, (3) 817-830 , DOI
Belton A, Guillot D, Khare A & Putinar M (2016) 'Matrix positivity preservers in fixed dimension. I' Advances in Mathematics 298, 325-368 , DOI
Belton A, Guillot D, Khare A & Putinar M (2016) 'Matrix positivity preservers in fixed dimension' Comptes Rendus Mathematique 354, (2) 143-148 , DOI
Belton ACR & Wills SJ (2015) 'An algebraic construction of quantum flows with unbounded generators' Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, (1) , DOI
Belton ACR (2014) 'Quantum Random Walks with General Particle States' Communications in Mathematical Physics 328, (2) 573-596 , DOI
Belton ACR & Sinha KB (2014) 'STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES' The Quarterly Journal of Mathematics 65, (4) 1145-1164 , DOI
Belton ACR, Lindsay JM & Skalski AG (2013) 'Quantum Feynman-Kac perturbations' Journal of the London Mathematical Society 89, (1) 275-300 , DOI
Belton ACR (2010) 'Quantum Random Walks and Thermalisation' Communications in Mathematical Physics 300, (2) 317-329 , DOI
Belton ACR (2010) 'Random-walk approximation to vacuum cocycles' Journal of the London Mathematical Society 81, (2) 412-434 , DOI
Belton ACR (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
Attal S & Belton ACR (2007) 'The chaotic-representation property for a class of normal martingales' Probability Theory and Related Fields 139, (3-4) 543-562 , DOI
BELTON ACR (2006) 'SOME SELF-ADJOINT QUANTUM SEMIMARTINGALES' Proceedings of the London Mathematical Society 92, (3) 791-816 , DOI
Belton ACR (2004) 'Erratum' The Quarterly Journal of Mathematics 55, (4) 505-505 , DOI
Belton ACR (2004) 'An Isomorphism of Quantum Semimartingale Algebras' The Quarterly Journal of Mathematics 55, (2) 135-165 , DOI
Belton ACR (2001) 'Quantum Ω-Semimartingales and Stochastic Evolutions' Journal of Functional Analysis 187, (1) 94-109 , DOI
Chapters
Belton A, Guillot D, Khare A & Putinar M (2019) 'A Panorama of Positivity. I: Dimension Free' Trends in Mathematics Springer International Publishing 117-165 , DOI
Belton ACR (2019) 'Introduction to Classical and Quantum Markov Semigroups' Open Quantum Systems Springer International Publishing 1-54 , DOI
BELTON ACR (2008) 'APPROXIMATION VIA TOY FOCK SPACE — THE VACUUM-ADAPTED VIEWPOINT' WORLD SCIENTIFIC , DOI
BELTON ACR (2005) 'A NOTE ON VACUUM-ADAPTED SEMIMARTINGALES AND MONOTONE INDEPENDENCE' WORLD SCIENTIFIC , DOI
Conference Papers
Belton A, Guillot D, Khare A & Putinar M (2016) 'Schur polynomials and matrix positivity preservers' 155-166
BELTON ACR (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