Applied and Nonlinear Analysis Program

This Program is currently coordinated by Prof. Neil Trudinger.

Research

Current research in the programme emphasizes nonlinear partial differential equations and differential geometry, along with applications and relevant computation.

The main (interrelated) topics of research are:

- Elliptic and parabolic partial differential equations,

- Geometric and physical variational problems,

- Geometric partial differential equations,

- Geometric evolutions,

- Geometric measure theory,

- Optimal transportation,

- Affine differential geometry,

- Conformal differential geometry,

- Finite element and difference equation approximations.

Highlights

In recent years, members of the programme have solved major open problems in curvature flow, affine geometry and optimal transportation, using techniques from nonlinear partial differential equations. The first complete proof, for more than two dimensions, of the famous 200 year old Monge problem of mass transfer was found by programme members in 2001.

The programme currently accounts for three ARC Large Programme Grants and one ARC Postdoctoral Fellowship.

Trudinger (1981) was the first recipient of the Australian Mathematical Society Medal for research. Andrews (2003), Urbas (1999), and Wang (2002) were also recipients of the Medal. Recent honours also include invited talks at the 2002 International Congress of Mathematicians (Andrews and Wang) and the 2006 International Congress of Mathematicians (Trudinger).

Study

Honours and Ph.D supervision can be provided in areas listed in Research.

Events

Forthcoming events

11/12-15/12, 2006, 8th Pacific Rim Geometric Conference Murramarang Resort, South Durras, NSW, Australia,

Previous events

23/5-10/6, 2005, International Workshop on Fully Nonlinear PDE and Applications Zhejiang University, China

People

Ben Andrews
(Differential geometry and P. D. E.)
Michael F. Barnsley
(Dynamical systems, fractal geometry, digital imaging)
Florica Cirstea
(Semilinear elliptic P. D. E., singular behaviour and boundary value problems)
Julie Clutterbuck
(Differential geometry and P. D. E.)
Algy Howe
(Stability of systems of O. D. E.)
John Hutchinson
(Finite element approximations for geometric problems, random fractals, geometric measure theory and geometric variational problems)
Seick Kim
(Regualrity theory for PDEs of elliptic and parabolic types, harmonic Analysis with applications to PDEs)
Neil Trudinger
(Elliptic P. D. E. and geometric applications)
John Urbas
(Elliptic and parabolic partial differential equations, Monge-Ampere equations)
Xu-Jia Wang
(Elliptic and parabolic equations, Monge-Ampere type equations, applications in geometry, optimal transportation. )
Qinghe Yin
(Fractal geometry, Communication traffic modelling.)

Graduate students associated with this program.

Jiakun Liu
Greg von Nessi
Huy Nguyen
Robert Scealy
Nigal Wilkin-Smith

Others associated with this program

Richard Melrose (MIT) Adjunct Professor
Robert Bartnik (Monash University)
Nirmalendu Chaudhuri (University of Wollongong)
Yi Fang (Centre for Bioinformation Science )
Andrew Hassell (Analysis and Geometry program)
Min-Chun Hong (University of Queensland)
Denis Labutin (University of California at Santa Barbara)
Alan McIntosh (Analysis and Geometry program)
Weimin Sheng (Zhejiang University)
Peter J. Vassiliou (University of Canberrra)
Bryan Wang (Analysis and Geometry program)