Ian Doust

Honorary Associate Professor

BSc W.Aust., MSc Tor., PhD Edin., FAustMS

Contact information

Office: Room 6113, Red Centre
Email:
Telephone:: +61 - 2 - 9385 7097; +61 - 2 - 9385 7003 (Pure Mathematics Office)
Fax:: +61 - 2 - 9385 7123
Mail:: School of Mathematics and Statistics; University of New South Wales; UNSW Sydney, NSW, 2052; Australia

Research Interests

Much of my work is in the area of operator theory and the geometry of Banach spaces. In particular my work has concentrated on the relationships between functional calculus and integral representations for operators, and how this is affected by geometric properties of the spaces on which the operators act. More recently I have been investigating geometric properties of metric spaces.

Students

Having retired, I am not currently accepting new students. Here is a list of my past graduate students.

PhD students

1998 Qingping Cheng, "Well-bounded operators on general Banach spaces". (at Murdoch University, co-supervised with Ken Harrison)
1999 Brenden Ashton, "Functions of bounded variation in two variables and AC(σ) operators".
2006 Venta Terauds, "Extensions of functional calculus for Banach space operators".
2014 Stephen Sánchez, "The p-negative type of finite metric spaces".
2020 Raveen de Silva, "Maximum generalised roundness of graph metric spaces".
2020 Shaymaa Al-sharkarchi, "Isomorphisms of BV(σ) and AC(σ) spaces".
2023 Gavin Robertson, "Roundness, negative type and bi-lipschitz embeddings into Hilbert space".
2023 Alan Stoneham, "AC(σ) operators and functions of bounded variation".

Masters students

1993 Eveline Hutahaean, M.Math., "Contractive projections on Banach spaces".
2006 Michael Anderson, M.ScTech., "Uniform classification of metric spaces".
2016 Louise Wilkinson, M.Sc., "Exchangeability and G-measures".
2022 Peter Hehir, M.Math., "Dvoretzky's Theorem".

Honours students

1997 Brendan Litton, "The unconditional basic sequence problem".
2003 Robert Taggart, "Harmonic analysis in UMD spaces".
2003 Ronny Lan, "Almost commuting Hermitian matrices are near commuting Hermitian matrices".
2005 Wil Soo, "Contractive projections in L^p".
2007 Beren Sanders, "The Buseman-Petty problem in convex geometry". (University Medal)
2009 Daniel Gow, "C^*-algebras associated to directed graphs and labelled graphs". (co-supervised with Teresa Bates)
2010 Jessica Egan (now Hamby), "Semigroups of composition operators".
2015 Dominic Vella, "Modern harmonic analysis and the T(1) Theorem".
2015 Stuart Hatzioannou, "Index theory".
2015 Raveen de Silva, "Composition C^*-algebras".
2017 Matthew Hircock, "The numerical range and block numerical range of linear operators".
2018 Alan Stoneham, "Toeplitz operators on a Hilbert space of analytic functions". (University Medal)
2018 Gavin Robertson, "Numerical invariants of Banach and metric spaces". (University Medal)
2019 Harry Denman, "The fixed point property for nonexpansive mappings in Banach spaces"
2021 Daniel Czapski, "Aysmptotic eigenvalue distributions of Gaussian Hermitian random matrices"

Short Biography

Born and bred in Perth, Western Australia, I completed a BSc(Hons) in Pure Mathematics in 1982. After 2 years working as a mathematician and programmer for a surveying company I returned to study in 1984. I completed an MSc at the University of Toronto under the supervision of Peter Rosenthal in 1985 before going to Edinburgh to start a PhD with Alastair Gillespie . My PhD was awarded in 1988 for a thesis entitled "Well-bounded operators and the geometry of Banach spaces".

On completing my PhD I returned to Australia to a postdoctoral position at Macquarie University working with Alan McIntosh. In 1989 I was lured to the other side of Sydney to take up a lectureship at UNSW.

I retired in 2023, but am still active in the school.

Publications

Many of my publications are available on-line.