We have a wide range of potential research topics. They range from short term PhB projects, to year long Honours and graduate projects and three year PhD projects.
Contact your supervisor for further discussion and ideas.

### Efficient numerical methods for 3D underwater acoustic wave propagation

Efficient numerical methods for 3D underwater acoustic wave propagation

#### Student intake

Open for Honours, Masters, Summer scholar students

#### People

Adaptive sparse grids automatically search for the best resolution in each dimension and build a model of the data. This project will study techniques, implementations and merits of such adaptive schemes for use in predictive modelling using sparse grids.

#### Student intake

Open for Honours students

#### People

Our projects cover computational methods used in biology, chemistry, physics, finance and machine learning. They prepare applied and pure mathematicians for collaborative work with scientists and engineers and for doing a PhD in this area.

#### Student intake

Open for Bachelor, Honours students

### Algebraic topology

Depending on student interest and background I can supervise a variety of topics related to algebraic topology.

#### Student intake

Open for Bachelor, Summer scholar students

### Analysis (harmonic, functional, and/or stochastic) of partial differential equations

Analysis (harmonic, functional, and/or stochastic) of partial differential equations.

#### Student intake

Open for Bachelor, Honours, Masters, PhD students

### Ancient solutions to geometric flows

Ancient solutions to geometric flows

#### Student intake

Open for Summer scholar students

### Applications of geometric flows in geometry

Applications of geometric flows in geometry

#### Student intake

Open for Summer scholar students

### Arithmetic algebraic geometry

Arithmetic algebraic geometry

#### Student intake

Open for Summer scholar students

### Arithmetic and Geometry over Finite Fields

How many solutions does the equation x2+y2 = z2 have if x, y, z are taken from Z/pZ? How many square-free polynomials of degree n are there with coefficients in Z/pZ? Questions of this kind have deep and seemingly unexpected connections with the arithmetic and geometry of algebraic varieties.

#### Student intake

Open for Honours, Masters, PhD students

### Circularly polarised radiation in early proto-planetary systems

The discovery of strong 17 per cent circular polarisation in the IR in the Orion OMC-1 star forming region has provided a new impetus to the view that the homochirality of natural amino-acids seen in biological systems on Earth may have been triggered by asymmetric photolysis of biogenic amino acids in space.

#### Student intake

Open for PhD students

### Clustering techniques

Clustering, ie finding groups of similar objects, is a central theme in data mining. While the k-means algorithm is one of the most popular at the moment, strong contenders are based on the estimation of density

#### Student intake

Open for Honours students

### Combinatorial and Geometric Group Theory

Combinatorial and Geometric Group Theory

#### Student intake

Open for Honours, Masters, PhD students

### Compact binary stars

About 50 percent of stars in our Galaxy occur in binary systems. The orbits of such systems evolve with time due to a variety of mechanisms involving mass and angular momentum loss.

#### Student intake

Open for PhD students

### Complex cobordism & stable homotopy

Homotopy groups are extremely difficult to compute, and even the homotopy groups of spheres are only understood through some small range of degrees.

#### Student intake

Open for Honours, Masters students

### Computability in Algebra and Geometry

Can one write a computer program to decide whether two given rings are isomorphic? Or whether a given group is the trivial group? Or whether a given CW complex is a sphere? These are questions on the inteface of logic, theoretical computer science, and mathematics with fascinating results and open problems.

#### Student intake

Open for Honours, Masters, PhD students