About me
Present Appointment:
Professor of Mathematical Physics,
University of Glasgow
ian.strachan@glasgow.ac.uk
Other Positions/Activities:

20182023: Head of School, School of Mathematics and Statistics, University of Glasgow

20152017: President, Edinburgh Mathematical Society
and exofficio member of the UK’s
Council for the Mathematical Sciences

20152018: Member of the UK’s Engineering and Physical Sciences Research Council (EPSRC) Strategic Advisory Team for the Mathematical Sciences

2003present: Member of the EPSRC peer review college

20062010: Associate Dean (Postgraduate) and Head of the Faculty
Graduate School

20082009: Convenor of the University’s Heads of Graduate Schools Forum
Editorial Activities:

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

Former EditorinChief, 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;
 biHamiltonian 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 
Publications
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.
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Older publications

How to count curves: from nineteenth century problems to twentyfirst century Solutions,
Phil. Trans. R. Soc. Lond. A 361 (2003) 26332648.

Frobenius manifolds and the biHamiltonian structure on discriminant hypersurfaces,
In Integrable Systems, Topology and Physics
Amer.Math.Soc. Contemporary Mathematics series 309 (2002) 251265

Unitized Jordan algebras and dispersionless KdV equations
(coauthor O.D.McCarthy)
J. Phys. A 34 (2001) 24352442.

Degenerate biHamiltonian structures
Teoreticheskaya i Matematicheskaya Fizika
(republished in Theoretical and Mathematical Physics 122:2 (2000) 247255)

On the integrability of a thirdorder MongeAmpere type Equation,
Physics Letters A 210 (1996) 267272

KahlerEinstein metrics with SU(2) action,
(coauthor: A.S.Dancer)
Math. Proc. Camb. Phil. Soc. 115 (1994) 513525

Moduli Space Metrics for Axially Symmetric Instantons,
Proc. Roy. Soc. A 446 (1994) 479497

Hierarchy of Conserved Currents for SelfDual Einstein Spaces,
Classical and Quantum Gravity 10 (1993) 14171423

Some Integrable Hierarchies in (2+1)Dimensions and their Twistor Description,
Journal of Mathematical Physics 34 (1993) 243259

Wave Solutions of a (2+1)Dimensional generalisation of the NonLinear Schrodinger Equation,
Inverse Problems 8 (1992) L21L27

The Moyal Algebra and Deformations of the SelfDual Einstein Equations,
Physics Letters B 283 (1992) 6366

A New Family of Integrable Models in (2+1)Dimensions Associated with Hermitian Symmetric Spaces,
Journal of Mathematical Physics 33 (1992) 24772482

LowVelocity Scattering of Vortices in a modified Abelian Higgs Model,
Journal of Mathematical Physics 33 (1992) 102110

SelfDual Gauge Fields and the NonLinear Schrodinger Equation,
Physics Letters A 154 (1991) 123126
Research
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: extendedaffine orbit spaces and associated Frobenius manifolds, symmetries of Frobenius manifolds and related structures; biHamiltonian 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 DonaldsonThomas 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.