About me

Present Appointment:

Professor of Mathematical Physics, University of Glasgow


Other Positions/Activities:

  • 2018-2023: Head of School, School of Mathematics and Statistics, University of Glasgow

  • 2015-2017: President, Edinburgh Mathematical Society and ex-officio member of the UK’s Council for the Mathematical Sciences

  • 2015-2018: Member of the UK’s Engineering and Physical Sciences Research Council (EPSRC) Strategic Advisory Team for the Mathematical Sciences

  • 2003-present: Member of the EPSRC peer review college

  • 2006-2010: Associate Dean (Postgraduate) and Head of the Faculty Graduate School

  • 2008-2009: Convenor of the University’s Heads of Graduate Schools Forum

Editorial Activities:

  • Editorial Advisor, Bulletin, Journal and Transactions of the London Mathematical Society

  • Former Editor-in-Chief, Glasgow Mathematical Journal

PhD Projects

I am always interested in hearing from students who might wish to undertake a PhD under my supervision. Please feel free to contact me directly. Possible topics include:

  • construction and properties of Frobenius manifolds;
  • bi-Hamiltonian structures;
  • deformations of integrability;
  • qDT invariants and deformations of hyperKahler geometry.

Current Students:

Alessandro Prosperio

Andre Bedell

Leo Kaminski (jointly supervised with Prof Misha Feigin)

Former Students:

Name Thesis Title
Georgios Antoniou (jointly supervised with Prof Misha Feigin) Frobenius structures, Coxeter discriminants, and supersymmetric mechanics
Richard Stedman Deformations, Extensions and Symmetries of Solutions to the WDVV equations
Ewan Morrison Modular Frobenius manifolds
James Ferguson Geometric structures on the tangent space of Hamiltonian evolution equations
Andrew Riley Frobenius manifolds: caustic submanifolds and discriminant almost duality
Kevin Baron Deformations of equations of hydrodynamic type
Oscar McCarthy Dispersionless Integrable Systems of KdV type


All my recent preprints and publications appear on ArXiv - the list below is automatically updated from there. For the published version, click on the DOI link at the end of each entry - this will take you to the published version but you will need library access to read them. Older papers are listed below.

Another source of information is my ORCID account.

[Loading myarticles...]

Older publications


My research interests are in integrable systems and mathematical physics. In particular I am interested in Frobenius manifolds and their applications. Such objects lie at the intersection of many areas of mathematics, from Topological Quantum Field Theories (TQFT’s), to quantum cohomology, singularity theory and mathematical physics.

Specific areas of interest are: extended-affine orbit spaces and associated Frobenius manifolds, symmetries of Frobenius manifolds and related structures; bi-Hamiltonian geometry and the deformation of dispersionless integrable systems. An informal introduction to the theory may be found here: What is a Frobenius Manifold

More recently I have become interested in Donaldson-Thomas invariants and hyperKahler geometry, and quantum DT invariants and integrable deformations of hyperKahler geometry.

The background image shows the zero set corresponding to a certain point in the versal deformation space of the E₆ elliptic singularity. This deformation space may be endowed with the structure of a Frobenius manifold.

I am a member of the Integrable Systems and Mathematical Physics research group within the School, and the Core Structures group.