Geometric and Nonlinear Analysis

Our research is concentrated on:

  • Nonlinear partial differential equations, in particular systems;
  • Dynamical systems;
  • Calculus of Variations;
  • Geometric evolution equations (in particular the harmonic map heat flow, Yang-Mills flow, and curvature flows);  

We consider a range of problems from very pure to vey applied, rom heoretical to computational. We have active collaborations with a number of groups inside Australia and around the world. Our members hold 4 current ARC Discovery Grants.
For more information please follow the links to people's personal web pages.
 

Staff

Professor Joseph Grotowski
Dr Cathy Holmes
Dr Min-Chun Hong
Dr Huy Nguyen
Dr Artem Pulemotov
Associate Professor Bevan Thompson
 

Honorary Staff

Dr Jan Chabrowski

Available Projects

Nonlinear Partial Differential Equations and Geometric Evolution Equations

A number of projects are offered in the areas of Nonlinear Partial Differential Equations and Geometric Evolution Equations. These include topics in partial regularity theory for elliptic and parabolic systems, the evolution equations associated with liquid crystals, Yang-Mills flow and work on...

Professor Joseph Grotowski

Markov Processes and Operator Theory: Convergence Rates for Markov Processes

This project concerns convergence rates for strongly ergodic Markov
processes. This work will provide the most general formulation of
convergence rates for Markov Chains for diffusions on the real line and for
diffusions on Riemannian manifolds. It will open up the possibility...

Professor Phil Pollett

Convolutions in the S-Plane with Applications

It is well known that the Laplace transform of a time-domain convolution of two functions is the product of the individual Laplace transforms.  A similar 'dual' property is that a convolution type contour integral of two Laplace transform yields the time domain product.  This...

Dr Yoni Nazarathy

Geometric PDE: Prescribed Curvature Problems, the Ricci Flow, and Yang-Mills Theory

There are multiple projects available in the field of geometric partial differential equations. Most of these projects focus on prescribed curvature problems, the Ricci flow, and Yang-Mills theory. The questions they address are related to general relativity, quantum field theory, and other...

Dr Artem Pulemotov

Stochastic Differential Geometry: Probabilistic Approaches to Geometric Problems

Several projects are offered in the area of stochastic differential geometry. These projects pursue two interconnected goals. On the one hand, they are to develop a better understanding of stochastic processes on Riemannian manifolds. On...

Dr Artem Pulemotov

Geometric Flows

The field of geometric flows has seen significant recent activity with notable achievements such as the resolution of the geometrization conjecture, Poincaré's ...

Dr Huy Nguyen

Surfaces with Critical Curvature Bounds

Surfaces are 2-dimensional objects that play a fundamental role in differential geometry and its applications. When surfaces are immersed in an ambient space they have a natural associated energy called the Willmore energy (or the elastic...

Dr Huy Nguyen
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