Professor Alexander Belton CMath, CSci, FIMA, SFHEA
Visiting ProfessorResearch Interests
My research takes place within two fields: quantum probability, a branch of mathematics involving functional analysis, probability theory and quantum mechanics, and matrix positivity, an area of linear algebra with diverse applications.
Research Grants
- Leverhulme Trust RPG-2014-196 Quantum Random Walks and Quasi-free Quantum Stochastic Calculus (January 2014 - January 2016)
Current Teaching
- MATH412 Topology and Fractals
Professional Role
- Departmental representative and Northwest Branch committee member for the Institute of Mathematics and its Applications
- Deputy Head of Department (January - August 2017)
- Head of Pure Mathematics Section (January - August 2017)
- Head of Undergraduate Teaching (Lent Term 2015)
- Head of Undergraduate Admissions (August 2008 - August 2012)
- Part I Director of Studies (September 2013 - August 2017)
- Departmental representative and Northern Regional Committee member for the London Mathematical Society (March 2012 - August 2017)
PhD Supervisions Completed
- Michał Gnacik (2010-14)
- Jason Hancox (2014-18)
PhD Supervision Interests
Applications to join the department's thriving PhD programme are welcome from students with interests in analysis, probability theory or mathematical physics. The area in which I work, non-commutative probability, is an exciting combination of these three subjects. Knowledge of all of them is not necessary, but an interest to discover more is.
At present I'm particularly interested in the following topics.
- Quantum random walks. A classical random walk consists of repeatedly flipping a coin and moving left or right accordingly. This simple model illustrates many important ideas in probability theory. Its quantum generalisation corresponds to a system interacting with a sequence of identical particles; limit theorems have been obtained, but many interesting questions remain unanswered.
- Non-commutative stopping times. Stopping times are random times which, at any given moment, are known to have occurred or not. The time of the first rainfall this week is a stopping time; the time of the last rainfall is not. The theory of stopping times is vital for developing classical theories of stochastic integration. The proper non-commutative generalisation is known, but is yet to be exploited fully.
- Exotic forms of independence. The concept which separates probability from analysis is stochastic independence. Once one moves to the non-commutative world, more than one form of independence exists. Free independence was introduced by Voiculescu in the 1980s, and has important connections to random matrix theory, quantum information theory and representation theory. Connections for other forms of independence remain to be explored.
Mathematical Sciences RA
01/04/2021 → 31/12/2023
Research
Applied Matrix Positivity
01/03/2021 → 30/06/2021
Research
An introduction to quantum filtering
24/06/2019 → 13/09/2019
Research
Quantum Random Walks and Quasi-Free Quantum Stochastic Calculus
05/01/2015 → 04/01/2017
Research
New Challenges in Operator Semigroups conference
Participation in conference - Academic
2022 Meeting of the International Linear Algebra Society
Participation in conference -Mixed Audience
Mathematical Sciences Seminar, University College Cork
Participation in workshop, seminar, course
Positivity Problems Associated to Permutation Patterns
Participation in workshop, seminar, course
Functional Analysis Seminar, University of Oxford
Participation in workshop, seminar, course
HoDoMS Annual Conference and AGM
Participation in conference -Mixed Audience
Analysis and Probability Research Group Seminar, Indian Institute of Science, Bangalore
Participation in workshop, seminar, course
LMS Annual General Meeting
Participation in workshop, seminar, course
University of Delhi (External organisation)
Membership of committee
Manchester Metropolitan University
Visiting an external academic institution
Mediterranean Journal of Mathematics (Journal)
Publication peer-review
Infinite Dimensional Analysis, Quantum Probability and Related Topics (Journal)
Editorial activity
University Kebangsaan Malaysia
Visiting an external academic institution
Journal of Statistical Physics (Journal)
Publication peer-review
OfS digital teaching and learning review: STEM expert workshop
Participation in workshop, seminar, course
Engineering and Physical Sciences Research Council (External organisation)
Membership of committee
Annali di Matematica Pura ed Applicata (Journal)
Publication peer-review
Portsea Maths Research Webinar
Participation in workshop, seminar, course
ATLAS Reviewing and Support briefing session
Participation in workshop, seminar, course
HoDoMS Annual Conference and AGM
Participation in conference -Mixed Audience
PhD external examiner
Examination
Celebrating Diverse and Inclusive Leaders from the N8 Partnership
Participation in workshop, seminar, course
AdvanceHE Professional Development Course for External Examiners
Participation in workshop, seminar, course
Engineering and Physical Sciences Research Council (External organisation)
Membership of committee
Special Matrices (Journal)
Publication peer-review
40th International Conference on Quantum Probability and Infinite Dimensional Analysis
Participation in conference -Mixed Audience
Annales Henri Poincaré (Journal)
Publication peer-review
NBFAS Meeting, Lancaster University
Participation in workshop, seminar, course
British Mathematical Colloquium
Participation in conference -Mixed Audience
HoDoMS Annual Conference and AGM
Participation in conference -Mixed Audience
EPSRC Mathematical Sciences Heads of Department meeting
Participation in workshop, seminar, course
Mathematics Colloquium, Swansea University
Participation in workshop, seminar, course
Mathematics Seminar, Indian Institute of Science, Bangalore
Participation in workshop, seminar, course
Conference on Recent Advances in Operator Theory and Operator Algebras 2018
Participation in conference -Mixed Audience
Indian Institute of Science, Bangalore
Visiting an external academic institution
Bangor University
Visiting an external academic institution
LMS Annual General Meeting and Naylor Lecture
Participation in workshop, seminar, course
NBFAS Meeting, University of Oxford
Participation in workshop, seminar, course
CMO-BIRS Workshop on Quantum Transport Equations and Applications
Participation in workshop, seminar, course
Bangor University International College
Visiting an external academic institution
18th Workshop: Noncommutative Probability, Operators Algebras, Random Matrices and Related Topics, with Applications
Participation in conference -Mixed Audience
Department for Education (External organisation)
Membership of committee
LMS Hardy Lecture and Society Meeting
Participation in workshop, seminar, course
NBFAS Meeting, Newcastle University
Participation in workshop, seminar, course
University of Brighton (External organisation)
Membership of committee
HoDoMS Annual Conference and AGM
Participation in conference -Mixed Audience
NBFAS 50th Anniversary Meeting
Participation in conference -Mixed Audience
Lancaster Analysis Days 2018
Participation in conference -Mixed Audience
Discussion meeting on foundations of quantum mechanics and their impact on contemporary society
Participation in conference -Mixed Audience
Journal of Applied Analysis (Journal)
Publication peer-review
EPSRC Mathematical Sciences Heads of Department meeting
Participation in workshop, seminar, course
Physica A: Statistical Mechanics and its Applications (Journal)
Publication peer-review
2017 Meeting of the International Linear Algebra Society
Participation in conference -Mixed Audience
IMA Annual General Meeting and Gold Medal Lecture
Public Lecture/ Debate/Seminar
Combinatorial Techniques in Analysis and Probability meeting
Participation in conference -Mixed Audience
Mathematics Seminar, Indian Institute of Science, Bangalore
Participation in workshop, seminar, course
Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Visiting an external academic institution
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 -Mixed Audience
University of Göttingen
Visiting an external academic institution
Conference on Invariant Subspaces and Banach Algebras
Participation in conference -Mixed Audience
International Journal of Analysis (Journal)
Publication peer-review
International Centre for Mathematical Sciences
Visiting an external academic institution
LMS Hardy Lecture and Society Meeting
Participation in workshop, seminar, course
LMS Northern Regional Meeting, University of Manchester
Participation in conference -Mixed Audience
SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) (Journal)
Publication peer-review
Institut Camille Jordan, Université Claude Bernard Lyon 1 (External organisation)
Membership of committee
NBFAS Meeting, Queen's University Belfast
Participation in workshop, seminar, course
Discussion meeting on quantum technology for the 21st century
Participation in conference -Mixed Audience
Analysis Seminar, University of Glasgow
Participation in workshop, seminar, course
UK Easter Probability Meeting 2016
Participation in conference -Mixed Audience
Hindustan Book Agency (Publisher)
Publication peer-review
Scottish Operator Algebras Research meeting
Participation in conference -Mixed Audience
LMS Mary Cartwright Lecture and Society Meeting
Participation in workshop, seminar, course
Indian Statistical Institute (Bangalore Centre)
Visiting an external academic institution
Tbilisi Mathematical Journal (Journal)
Publication peer-review
Advances in Difference Equations (Journal)
Publication peer-review
Sheffield Probability Day
Participation in workshop, seminar, course
George Boole Mathematical Sciences Conference
Participation in conference -Mixed Audience
Differential Equations and Applications (Journal)
Publication peer-review
QOP Meeting in Warsaw, Quantum Probability, Groups and Geometry
Participation in conference -Mixed Audience
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 -Mixed Audience
Conference on Recent Advances in Operator Theory and Operator Algebras 2014
Participation in conference -Mixed Audience
Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Visiting an external academic institution
Journal of Theoretical Probability (Journal)
Publication peer-review
NBFAS Meeting, University of Leeds
Participation in workshop, seminar, course
EPJ Quantum Technology (Journal)
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 (Journal)
Publication peer-review
QOP Meeting in Lancaster
Participation in conference -Mixed Audience
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 -Mixed Audience
EDT Headstart Summer School
School Engagement
University College Cork
Visiting an external academic institution
NBFAS Meeting, University of Glasgow
Participation in workshop, seminar, course
Springer (Publisher)
Publication peer-review
Young Functional Analysts' Workshop 2014
Participation in conference -Mixed Audience
Sheffield Probability Day 2014
Participation in conference -Mixed Audience
Qymru Workshop on Open Quantum Systems and Quantum Control
Participation in workshop, seminar, course
LMS Northern Regional Meeting, Durham University
Participation in conference -Mixed Audience
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 -Mixed Audience
Mathematical Communications (Journal)
Publication peer-review
Noncommutative Geometry Seminar, Mathematical Institute of the Polish Academy of Sciences
Participation in workshop, seminar, course
Polish Academy of Sciences
Visiting an external academic institution
Sheffield Probability Day 2013
Participation in conference -Mixed Audience
QOP Meeting in Leeds, Quantum (semi)groups and (co)actions.
Participation in conference -Mixed Audience
QOP Meeting in Warsaw, Banach Algebras and C* Algebras
Participation in conference -Mixed Audience
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 -Mixed Audience
NBFAS Meeting, University of Sheffield
Participation in workshop, seminar, course
LMS Northern Regional Meeting, Newcastle University
Participation in conference -Mixed Audience
University College Cork
Visiting an external academic institution
Sheffield Probability Day 2012
Participation in conference -Mixed Audience
University College Cork (External organisation)
Membership of committee
NBFAS Meeting, Newcastle University
Participation in workshop, seminar, course
33rd International Conference on Quantum Probability and Related Topics
Participation in conference -Mixed Audience
Ulverston Victoria High School
School Engagement
Indiana University Mathematics Journal (Journal)
Publication peer-review
Workshop on Probabilistic Methods in Quantum Mechanics
Participation in workshop, seminar, course
Routledge (Publisher)
Publication peer-review
Functional Analysis Seminar, Université de Franche-Comté
Participation in workshop, seminar, course
Université de Franche-Comté
Visiting an external academic institution
Guernsey Grammar School
School Engagement
Elizabeth College, Guernsey
School Engagement
Hautlieu School, Jersey
School Engagement
NBFAS Meeting, University of Oxford
Participation in workshop, seminar, course
The Big Bang Fair 2012
Festival/Exhibition/Concert
Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences (Journal)
Publication peer-review
Conference on Quantum Probability, Noncommutative Geometry and Quantum Information
Participation in conference -Mixed Audience
Theo Murphy International Scientific Meeting on Principles and Applications of Quantum Control Engineering
Participation in conference -Mixed Audience
Sheffield Probability Day 2011
Participation in conference -Mixed Audience
Indian Statistical Institute Colloquium
Participation in workshop, seminar, course
Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore
Visiting an external academic institution
Journal of Mathematical Physics (Journal)
Publication peer-review
Indian Statistical Institute (Bangalore Centre) (External organisation)
Membership of committee
School
School Engagement
32nd International Conference on Quantum Probability and Related Topics
Participation in conference -Mixed Audience
Guernsey Grammar School
School Engagement
Hautlieu School, Jersey
School Engagement
Functional Analysis Seminar, Université de Franche-Comté
Participation in workshop, seminar, course
Université de Franche-Comté
Visiting an external academic institution
Indian Statistical Institute Colloquium
Participation in workshop, seminar, course
Indian Statistical Institute (Bangalore Centre)
Visiting an external academic institution
Zentralblatt MATH (Journal)
Publication peer-review
Analysis Seminar, Newcastle University
Participation in workshop, seminar, course
Minicourse on Financial Mathematics
Participation in workshop, seminar, course
Blackpool Sixth-Form College
School Engagement
Mathematische Nachrichten (Journal)
Publication peer-review
Irish Mathematical Society Meeting 2010
Participation in conference -Mixed Audience
University College Cork
Visiting an external academic institution
Communications on Stochastic Analysis (Journal)
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 (Journal)
Publication peer-review
Indian Statistical Institute (Bangalore Centre)
Visiting an external academic institution
Ballakermeen High School, Isle of Man
School Engagement
Ballakermeen High School, Isle of Man
School Engagement
University College Cork
Visiting an external academic institution
Analysis Seminar, University of Glasgow
Participation in workshop, seminar, course
30th International Conference on Quantum Probability and Related Topics
Participation in conference -Mixed Audience
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 -Mixed Audience
Stephen Wills
Hosting an academic visitor
Conference on Stochastic Differential Equations, Stochastic Partial Differential Equations and Related Topics
Participation in conference -Mixed Audience
Graham Jameson Meeting
Participation in conference -Mixed Audience
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 -Mixed Audience
University College Cork
Visiting an external academic institution
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 (Journal)
Publication peer-review
Operator Theory and Operator Algebras in Cork. A Conference in Memory of Gerard J Murphy
Participation in conference -Mixed Audience
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 -Mixed Audience
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 -Mixed Audience
Pure Mathematics Seminar, Lancaster University
Participation in workshop, seminar, course
27th International Conference on Quantum Probability and Related Topics
Participation in conference -Mixed Audience
Workshop on Quantum Probability and Its Applications
Participation in workshop, seminar, course
International Conference on Quantum Probability and Its Applications
Participation in conference -Mixed Audience
Probability Seminar, University College Cork
Participation in workshop, seminar, course
Bulletin of the London Mathematical Society (Journal)
Publication peer-review
Conference on Noncommutative Analysis, Quantum Theory and Stochastic Analysis
Participation in conference -Mixed Audience
Analysis Seminar, University of Nottingham
Participation in workshop, seminar, course
26th International Conference on Quantum Probability and Infinite Dimensional Analysis
Participation in conference -Mixed Audience
14th Évry-Nancy-Strasbourg Conference on Probability and Statistics
Participation in conference -Mixed Audience
7th Volterra-CIRM International School on Quantum Probability and Spectral Analysis on Large Graphs
Participation in conference -Mixed Audience
25th International Conference on Quantum Probability and Related Topics
Participation in conference -Mixed Audience
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 -Mixed Audience
University of Oxford (External organisation)
Membership of committee
Mathematical Reviews (Journal)
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 -Mixed Audience
Analysis Seminar, University of Nottingham
Participation in workshop, seminar, course
Conference on Quantum Probabilities and Paradoxes of the Quantum Century
Participation in conference -Mixed Audience
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 -Mixed Audience
Quantum Measure Theory meeting, Isaac Newton Institute
Participation in conference -Mixed Audience