# Dr Alexander Belton CMath, CSci, FIMA, SFHEA

Head of Department, Senior Lecturer in Pure Mathematics## Web Links

The cocycle identity holds under stopping

Belton, A.C.R., Sinha, K.B. 1/09/2017 In: The Quarterly Journal of Mathematics. 68, 3, p. 817-830. 14 p.

Journal article

Matrix positivity preservers in fixed dimension. I

Belton, A., Guillot, D., Khare, A., Putinar, M. 6/08/2016 In: Advances in Mathematics. 298, p. 325-368. 44 p.

Journal article

Matrix positivity preservers in fixed dimension

Belton, A., Guillot, D., Khare, A., Putinar, M. 02/2016 In: Comptes Rendus Mathématique. 354, 2, p. 143-148. 6 p.

Journal article

An algebraic construction of quantum flows with unbounded generators

Belton, A.C.R., Wills, S.J. 2015 In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 51, 1, p. 349-375. 27 p.

Journal article

The convergence of unitary quantum random walks

Belton, A.C.R., Gnacik, M., Lindsay, J.M. 25/04/2014 , 13 p.

Working paper

Quantum random walks with general particle states

Belton, A.C.R. 16/02/2014 In: Communications in Mathematical Physics. 328, 2, p. 573-596. 24 p.

Journal article

Stopping the CCR flow and its isometric cocycles

Belton, A.C.R., Sinha, K.B. 5/02/2014 In: The Quarterly Journal of Mathematics. 65, 4, p. 1145-1164. 20 p.

Journal article

Quantum Feynman-Kac perturbations

Belton, A.C.R., Lindsay, J.M., Skalski, A.G. 02/2014 In: Journal of the London Mathematical Society. 89, 1, p. 275-300. 26 p.

Journal article

On stopping Fock-space processes

Belton, A.C.R. 20/11/2013 , 40 p.

Working paper

A vacuum-adapted approach to quantum Feynman-Kac formulae

Belton, A.C.R., Lindsay, J.M., Skalski, A. 03/2012 In: Communications on Stochastic Analysis. 6, 1, p. 95-109. 15 p.

Journal article

Quantum random walks and thermalisation

Belton, A.C.R. 12/2010 In: Communications in Mathematical Physics. 300, 2, p. 317-329. 13 p.

Journal article

Random-walk approximation to vacuum cocycles

Belton, A.C.R. 04/2010 In: Journal of the London Mathematical Society. 81, 2, p. 412-434. 23 p.

Journal article

Approximation via toy Fock space - the vacuum-adapted viewpoint

Belton, A.C.R. 09/2008 In: Quantum Stochastics and Information. Singapore : World Scientific p. 3-22. 20 p. ISBN: 978-981-283-295-5.

Chapter

On the path structure of a semimartingale arising from monotone probability theory

Belton, A.C.R. 2008 In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 44, 2, p. 258-279. 22 p.

Journal article

The chaotic-representation property for a class of normal martingales

Belton, A.C.R., Attal, S. 1/11/2007 In: Probability Theory and Related Fields. 139, 3-4, p. 543-562. 20 p.

Journal article

Alicki-Fannes and Hudson-Parthasarathy evolution equations

Belton, A.C.R. 07/2007 In: Quantum Probability and Infinite Dimensional Analysis XX. Singapore : World Scientific p. 128-133. 6 p. ISBN: 978-981-270-851-9.

Chapter

Some self-adjoint quantum semimartingales

Belton, A.C.R. 1/05/2006 In: Proceedings of the London Mathematical Society. 92, 3, p. 791-816. 26 p.

Journal article

The monotone Poisson process

Belton, A.C.R. 2006 In: Quantum Probability. Warsaw : Polish Academy of Sciences p. 99-115. 17 p.

Chapter

A note on vacuum-adapted semimartingales and monotone independence

Belton, A.C.R. 01/2005 In: Quantum Probability and Infinite Dimensional Analysis XVIII. Singapore : World Scientific p. 105-114. 10 p. ISBN: 978-981-256-147-3.

Chapter

An isomorphism of quantum semimartingale algebras

Belton, A.C.R. 06/2004 In: The Quarterly Journal of Mathematics. 55, 2, p. 135-165. 31 p.

Journal article

Quantum Ω-semimartingales and stochastic evolutions

Belton, A.C.R. 1/12/2001 In: Journal of Functional Analysis. 187, 1, p. 94-109. 16 p.

Journal article

A matrix formulation of quantum stochastic calculus

Belton, A.C.R. 1998 University of Oxford. 110 p.

Doctoral Thesis

Quantum Random Walks and Quasi-Free Quantum Stochastic Calculus

05/01/2015 → …

Research

2017 Meeting of the International Linear Algebra Society

Participation in conference

IMA Annual General Meeting and Gold Medal Lecture

Public lecture/debate/seminar

Combinatorial Techniques in Analysis and Probability meeting

Participation in conference

Mathematics Seminar, Indian Institute of Science, Bangalore

Participation in workshop, seminar, course

Research visit to the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Research and Teaching at External Organisation

NBFAS Meeting, University of Birmingham

Participation in workshop, seminar, course

Mathematics Ancient and Modern outreach talk

Public lecture/debate/seminar

Scottish Operator Algebras Research meeting

Participation in conference

Introduction to Classical and Quantum Markov Semigroups lecture course

Research and Teaching at External Organisation

Conference on Invariant Subspaces and Banach Algebras

Participation in conference

International Journal of Analysis

Publication peer-review

Research visit to the International Centre for Mathematical Sciences, Edinburgh

Research and Teaching at External Organisation

LMS Hardy Lecture and Society Meeting

Participation in workshop, seminar, course

LMS Northern Regional Meeting, University of Manchester

Participation in conference

External examiner, Ph.D., Université Claude Bernard Lyon 1

Membership of peer review panel or committee

SIGMA (Symmetry, Integrability and Geometry: Methods and Applications)

Publication peer-review

NBFAS Meeting, Queen's University Belfast

Participation in workshop, seminar, course

Discussion meeting on quantum technology for the 21st century

Participation in conference

Analysis Seminar, University of Glasgow

Participation in workshop, seminar, course

UK Easter Probability Meeting 2016

Participation in conference

Hindustan Book Agency

Publication peer-review

Scottish Operator Algebras Research meeting

Participation in conference

LMS Mary Cartwright Lecture and Society Meeting

Participation in workshop, seminar, course

Research visit to Indian Statistical Institute, Kolkata, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore and Indian Statistical Institute, Bangalore

Research and Teaching at External Organisation

Tbilisi Mathematical Journal

Publication peer-review

Advances in Difference Equations

Publication peer-review

Sheffield Probability Day

Participation in workshop, seminar, course

George Boole Mathematical Sciences Conference

Participation in conference

Differential Equations and Applications

Publication peer-review

QOP Meeting in Warsaw, Quantum Probability, Groups and Geometry

Participation in conference

Newcastle University Spring School on Several Complex Variables

Participation in workshop, seminar, course

NBFAS Meeting, University of Edinburgh

Participation in workshop, seminar, course

LMS Mary Cartwright Lecture and Society Meeting

Participation in workshop, seminar, course

London Mathematical Society 150th Anniversary Launch

Public lecture/debate/seminar

QOP Meeting in Leeds

Participation in conference

Conference on Recent Advances in Operator Theory and Operator Algebras 2014

Participation in conference

Research visit to the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Research and Teaching at External Organisation

Journal of Theoretical Probability

Publication peer-review

NBFAS Meeting, University of Leeds

Participation in workshop, seminar, course

EPJ Quantum Technology

Publication peer-review

Workshop on Positivity, Graphical Models, and Modeling of Complex Multivariate Dependencies, American Institute of Mathematics

Participation in workshop, seminar, course

Journal of Mathematical Analysis and Applications

Publication peer-review

QOP Meeting in Lancaster

Participation in conference

Quantum Control Engineering: Mathematical Solutions for Industry (Open for Business event)

Participation in workshop, seminar, course

Quantum Control Engineering: Mathematical Principles and Applications

Participation in conference

Topology talk and Classifying the Alphabet Topologically mini-project

Schools engagement

Research visit to University College Cork

Research and Teaching at External Organisation

NBFAS Meeting, University of Glasgow

Participation in workshop, seminar, course

Springer

Publication peer-review

Young Functional Analysts' Workshop 2014

Participation in conference

Sheffield Probability Day 2014

Participation in conference

Qymru Workshop on Open Quantum Systems and Quantum Control

Participation in workshop, seminar, course

LMS Northern Regional Meeting, Durham University

Participation in conference

NBFAS Meeting, University of Edinburgh

Participation in workshop, seminar, course

Workshop and Conference in Honour of Professor K. B. Sinha's 70th Birthday

Participation in conference

Mathematical Communications

Publication peer-review

Noncommutative Geometry Seminar, Mathematical Institute of the Polish Academy of Sciences

Participation in workshop, seminar, course

Research visit to the Mathematical Institute of the Polish Academy of Sciences, Warsaw

Research and Teaching at External Organisation

Sheffield Probability Day 2013

Participation in conference

QOP Meeting in Leeds, Quantum (semi)groups and (co)actions.

Participation in conference

QOP Meeting in Warsaw, Banach Algebras and C^{*} Algebras

Participation in conference

Workshop on Quantum Probability, Statistics and Control

Participation in workshop, seminar, course

Functional Analysis Seminar, University of Oxford

Participation in workshop, seminar, course

NBFAS Meeting, Lancaster University

Participation in workshop, seminar, course

LMS Scheme 3 Meeting - Probability and Noncommutative Harmonic Analysis

Participation in workshop, seminar, course

QOP Meeting in Lancaster, Banach and Operator Spaces

Participation in conference

NBFAS Meeting, University of Sheffield

Participation in workshop, seminar, course

LMS Northern Regional Meeting, Newcastle University

Participation in conference

Research visit to University College Cork

Research and Teaching at External Organisation

Sheffield Probability Day 2012

Participation in conference

External examiner, M.Sc. by research, University College Cork

Membership of peer review panel or committee

NBFAS Meeting, Newcastle University

Participation in workshop, seminar, course

33rd International Conference on Quantum Probability and Related Topics

Participation in conference

Studying Mathematics at University, sixth-form talk at Ulverston Victoria High School

Schools engagement

Indiana University Mathematics Journal

Publication peer-review

Workshop on Probabilistic Methods in Quantum Mechanics

Participation in workshop, seminar, course

Routledge

Publication peer-review

Functional Analysis Seminar, Université de Franche-Comté

Participation in workshop, seminar, course

Erasmus Teaching Mobility visit to Université de Franche-Comté, Besançon

Research and Teaching at External Organisation

Islands Project talk to sixth-form students, Elizabeth College, Guernsey

Schools engagement

Islands Project talk to sixth-form students, Guernsey Grammar School

Schools engagement

Islands Project talk to sixth-form students, Hautlieu School, Jersey

Schools engagement

NBFAS Meeting, University of Oxford

Participation in workshop, seminar, course

The Big Bang Fair 2012

Festival/Exhibition

Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences

Publication peer-review

Conference on Quantum Probability, Noncommutative Geometry and Quantum Information

Participation in conference

Theo Murphy International Scientific Meeting on Principles and Applications of Quantum Control Engineering

Participation in conference

Sheffield Probability Day 2011

Participation in conference

Indian Statistical Institute Colloquium

Participation in workshop, seminar, course

Research visit to the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore

Research and Teaching at External Organisation

Journal of Mathematical Physics

Publication peer-review

External examiner, Ph.D., Indian Statistical Institute

Membership of peer review panel or committee

Taster Day talk to sixth-form students

Schools engagement

32nd International Conference on Quantum Probability and Related Topics

Participation in conference

Islands Project talk to sixth-form students, Guernsey Grammar School

Schools engagement

Islands Project talk to sixth-form students, Hautlieu School, Jersey

Schools engagement

Functional Analysis Seminar, Université de Franche-Comté

Participation in workshop, seminar, course

Research visit to Université de Franche-Comté, Besançon

Research and Teaching at External Organisation

Indian Statistical Institute Colloquium

Participation in workshop, seminar, course

Research visit to Indian Statistical Institute, Bangalore

Research and Teaching at External Organisation

Zentralblatt MATH

Publication peer-review

Analysis Seminar, Newcastle University

Participation in workshop, seminar, course

Minicourse on Financial Mathematics

Participation in workshop, seminar, course

STEM Symposium talk, Blackpool Sixth-Form College

Schools engagement

Mathematische Nachrichten

Publication peer-review

Irish Mathematical Society Meeting 2010

Participation in conference

Research visit to University College Cork

Research and Teaching at External Organisation

Communications on Stochastic Analysis

Publication peer-review

Workshop on Probability, Statistics and Analysis on Groups

Participation in workshop, seminar, course

Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports

Publication peer-review

Research visit to Indian Statistical Institute, Bangalore

Research and Teaching at External Organisation

Islands Project talk to sixth-form students, Ballakermeen High School, Isle of Man

Schools engagement

Islands Project teachers masterclass, Ballakermeen High School, Isle of Man

Schools engagement

Research visit to University College Cork

Research and Teaching at External Organisation

Analysis Seminar, University of Glasgow

Participation in workshop, seminar, course

30th International Conference on Quantum Probability and Related Topics

Participation in conference

Stochastic Analysis Seminar, Loughborough University

Participation in workshop, seminar, course

Yorkshire Functional Analysis Seminar, University of Leeds

Participation in workshop, seminar, course

Conference on Stochastic Processes at the Quantum Level

Participation in conference

Research visit by Dr Stephen Wills, University College Cork

Hosting an academic visitor

Conference on Stochastic Differential Equations, Stochastic Partial Differential Equations and Related Topics

Participation in conference

Graham Jameson Meeting

Participation in conference

Workshop on Stochastics in the North-West

Participation in workshop, seminar, course

61st British Mathematical Colloquium and 22nd Annual Meeting of the Irish Mathematical Society

Participation in conference

Research visit to University College Cork

Research and Teaching at External Organisation

3rd International Workshop on Quantum Probability and its Applications

Participation in workshop, seminar, course

Quantum Stochastics and Information Seminar, University of Nottingham

Participation in workshop, seminar, course

Applied Mathematics Letters

Publication peer-review

Operator Theory and Operator Algebras in Cork. A Conference in Memory of Gerard J Murphy

Participation in conference

Institute of Mathematics and Physics Seminar, Aberystwyth University

Participation in workshop, seminar, course

Functional Analysis Seminar, University of Oxford

Participation in workshop, seminar, course

International Workshop on Quantum Probability and its Applications

Participation in workshop, seminar, course

School on Quantum Potential Theory

Participation in conference

Workshop on Perspectives in Probability Theory and its Connections with Science and Society

Participation in workshop, seminar, course

Belfast Functional Analysis Day

Participation in conference

Pure Mathematics Seminar, Lancaster University

Participation in workshop, seminar, course

27th International Conference on Quantum Probability and Related Topics

Participation in conference

Workshop on Quantum Probability and Its Applications

Participation in workshop, seminar, course

International Conference on Quantum Probability and Its Applications

Participation in conference

Probability Seminar, University College Cork

Participation in workshop, seminar, course

Bulletin of the London Mathematical Society

Publication peer-review

Conference on Noncommutative Analysis, Quantum Theory and Stochastic Analysis

Participation in conference

Analysis Seminar, University of Nottingham

Participation in workshop, seminar, course

26th International Conference on Quantum Probability and Infinite Dimensional Analysis

Participation in conference

14th Évry-Nancy-Strasbourg Conference on Probability and Statistics

Participation in conference

7th Volterra-CIRM International School on Quantum Probability and Spectral Analysis on Large Graphs

Participation in conference

25th International Conference on Quantum Probability and Related Topics

Participation in conference

Stochastic Calculus Seminar, Université Louis Pasteur Strasbourg 1

Participation in workshop, seminar, course

Functional Analysis Seminar, University of Oxford

Participation in workshop, seminar, course

24th International Conference on Quantum Probability and Infinite Dimensional Analysis

Participation in conference

Internal examiner, D.Phil, University of Oxford

Membership of peer review panel or committee

Mathematical Reviews

Publication peer-review

Workshop on Quantum Probability and Applications

Participation in workshop, seminar, course

Functional Analysis Seminar, University of Oxford

Participation in workshop, seminar, course

Analysis Seminar, University of Nottingham

Participation in workshop, seminar, course

Conference on Noncommutativity - Geometry and Probability

Participation in conference

Analysis Seminar, University of Nottingham

Participation in workshop, seminar, course

Conference on Quantum Probabilities and Paradoxes of the Quantum Century

Participation in conference

Summer School on Quantum Probability

Participation in workshop, seminar, course

Functional Analysis Seminar, University of Oxford

Participation in workshop, seminar, course

Quantum Probability Day, University of Nottingham

Participation in conference

Quantum Measure Theory meeting, Isaac Newton Institute

Participation in conference