Dr Ian McIntosh
BSc (Monash), DIC, PhD (London)
My research concentrates on the geometry of surfaces. Most of this involves understanding the construction of surfaces which embed or immerse into "nice ambient spaces" so that the surface possesses an attractive property, such as being an area minimizer, or having constant mean curvature (and natural, relevant, generalisations of these properties). This involves a combination of Riemann surface theory, Lie group theory and harmonic map theory (particularly, Riemannian twistor theory). Right now I'm interested in: the conformal geometry of surfaces in the 4-sphere, Willmore surfaces, minimal and Hamiltonian stationary Lagrangian surfaces, using minimal surfaces to understand representations of a surface group (fundamental group of a compact hyperbolic surface), the relationship between minimal surfaces and Higgs bundles.
Minimal Lagrangian surfaces in CH^2 and representations of surface groups into SU(2,1). Geometriae Dedicata. 162(1):67-93.. 2013.
The quaternionic KP hierarchy and conformally immersed 2-tori in the 4-sphere.. Tohoku Mathematical Journal. Second Series, 63(2):183-215.. 2011.
The classification of Hamiltonian stationary Lagrangian tori in CP^2 by their spectral data.. Manuscripta Mathematica. 135:437-468.. 2011.
The spectral data for Hamiltonian stationary Lagrangian tori in R^4. Differential Geometry and its Applications. 29(2). 2011.
Chair, MAGIC Programme Committee
Member, MAGIC Management Committee
MAGIC node manager
Member, Board of Studies for PGCAP
Department of Mathematics, University of York, Heslington, York, UK. YO10 5DD