Alexander Belton - 糖心vlog会员

Professor Alexander Belton CMath, CSci, FIMA, SFHEA

Visiting Professor

Research 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

Micha? 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.

01/04/2021 → 31/12/2023
Research

01/03/2021 → 30/06/2021
Research

24/06/2019 → 13/09/2019
Research

05/01/2015 → 04/01/2017
Research

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Participation in conference -Mixed Audience

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Editorial activity

Visiting an external academic institution

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Examination

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Publication peer-review

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Visiting an external academic institution

Participation in workshop, seminar, course

Visiting an external academic institution

Participation in conference -Mixed Audience

Membership of committee

Participation in workshop, seminar, course

Membership of committee

Participation in conference -Mixed Audience

Publication peer-review

Participation in workshop, seminar, course

Publication peer-review

Participation in conference -Mixed Audience

Public Lecture/ Debate/Seminar

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Visiting an external academic institution

Participation in workshop, seminar, course

Public Lecture/ Debate/Seminar

Participation in conference -Mixed Audience

Visiting an external academic institution

Participation in conference -Mixed Audience

Publication peer-review

Visiting an external academic institution

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Publication peer-review

Membership of committee

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Visiting an external academic institution

Publication peer-review

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Public Lecture/ Debate/Seminar

Participation in conference -Mixed Audience

Visiting an external academic institution

Publication peer-review

Participation in workshop, seminar, course

Publication peer-review

Participation in workshop, seminar, course

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

School Engagement

Visiting an external academic institution

Participation in workshop, seminar, course

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Publication peer-review

Participation in workshop, seminar, course

Visiting an external academic institution

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Visiting an external academic institution

Participation in conference -Mixed Audience

Membership of committee

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

School Engagement

Publication peer-review

Participation in workshop, seminar, course

Publication peer-review

Participation in workshop, seminar, course

Visiting an external academic institution

School Engagement

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Festival/Exhibition/Concert

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Participation in workshop, seminar, course

Visiting an external academic institution

Publication peer-review

Membership of committee

School Engagement

Participation in conference -Mixed Audience

School Engagement

Participation in workshop, seminar, course

Visiting an external academic institution

Participation in workshop, seminar, course

Visiting an external academic institution

Publication peer-review

Participation in workshop, seminar, course

School Engagement

Publication peer-review

Participation in conference -Mixed Audience

Visiting an external academic institution

Publication peer-review

Participation in workshop, seminar, course

Publication peer-review

Visiting an external academic institution

School Engagement

Visiting an external academic institution

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Hosting an academic visitor

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Visiting an external academic institution

Participation in workshop, seminar, course

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Publication peer-review

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Membership of committee

Publication peer-review

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

Participation in workshop, seminar, course

Participation in conference -Mixed Audience

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Contact Details

Department: School Of Mathematical Sciences
Office: B55, B - Floor, Fylde College
Telephone: +44 (0)1524 592371
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