Applied & nonlinear analysis

Applied & nonlinear analysis

Current research in the Applied & Nonlinear Analysis research program emphasises 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, and geometry of fractals.

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About

Current research in the Applied & Nonlinear Analysis research program emphasises:

  • 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
  • geometry of fractals.

Projects

The curve shortening flow is a simple and beautiful example of a geometric heat flow, the family of equations which includes the Ricci flow used by Perelman to prove the Poincare conjecture as well as many other interesting examples. 

Student intake

Open for Bachelor, Summer scholar course students

People

On a (compact) Riemannian manifold there is a natural differential operator on functions, the Laplacian. The eigenvalues of this operator are important invariants of the manifold, and there are many interesting results which relate the eigenvalues to other geometric quantities...

Student intake

Open for Bachelor, Summer scholar course students

People

A two dimensional Riemannian manifold is an abstract surface sitting nowhere in particular, but which somehow has the structures imposed on it that a surface gets by sitting in Euclidean space, such as tangent spaces, a metric etc.

Student intake

Open for Honours, Masters students

People

The LASSO and penalized likelihood methods have become an extremely hot topic in statistics over the past decade, as they offer a computationally efficient method of variable selection particularly in high dimensional situations.

Student intake

Open for Honours, Masters students

People

Minimal surfaces are surfaces which are critical points of the area functional, are are characterised by the vanishing of their mean curvature.

Student intake

Open for Bachelor, Summer scholar course students

People

The basic problem is to understand under what conditions it is possible to find a convex surface of prescribed Gauss curvature which also satisfies some boundary conditions.

Student intake

Open for Honours, Masters students

People

Members

Convenor

Professor

Emeritus

Michael Barnsley

Emeritus Professor

John Hutchinson

Emeritus Professor

Neil Trudinger

Emeritus Professor

Researcher

John Urbus

Emeritus Professor

Xu-Jia Wang

Professor

Student

News

The Antonio Ambrosetti medal is awarded for groundbreaking contributions to mathematical analysis.

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Professor Michael Barnsley has obtained the The Paul R. Halmos-Lester R. Ford Award for his paper “Self-Similar Polygonal Tiling.”

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