Title Project Discription Level Supervisor
Arithmetic of conics

The Birch and Swynnerton-Dyer conjecture is one of the million dollar problems for the 21st century as recognized by the Clay Institute. The conjecture concerns solutions of elliptic (genus 1) curves. Recently an analogy has been proposed for the much simpler case of genus 0 curves (conics)....

PhD Project Dr Victor Scharaschkin
Arithmetic of higher genus curves

Curves of genus 0 and 1 are relatively well understood. Starting in the 1990s explicit methods have been developed for the first time to deal with more complicated curves and determine all of their rational points. Open problems in this field include the role of an object called the Brauer-Manin...

PhD Project Dr Victor Scharaschkin
Euclidean rings

Euclidean rings are algebraic structures generalizing the set of integers. Like the integers they have a division algorithm and unique factorization. Historically it has proved very difficult to determine if a ring is Euclidean or not but there have been several recent breakthroughs which are...

PhD Project Dr Victor Scharaschkin
Computational number theory

There is also scope for work in computational number theory such as primality testing and factorization methods

PhD Project Dr Victor Scharaschkin
Neoclassical Invariant Theory

Using invariant theoretic approaches, you can study various geometric and combinatorial properties of finite-dimensional representations of the classical groups. A number of projects are available. Recent work in this area includes the study of flag/Grassmann varieties, toric degenerations,...

PhD Project Dr Sangjib Kim
The Positive Realization Problem

The Positive Realization Problem deals with finding descriptions of linear systems based on non-negative matrices.  It has applications in control, applied probability and statistics, yet is linear-...

Masters Project
Honours Project
Dr Yoni Nazarathy
Affine algebras and Langlands program

The Langlands program is one of the most ambitious research projects in mathematics. In the past decade it has become clear that representations of affine...

PhD Project Dr Masoud Kamgarpour
Root systems and their applications in representation theory

Root systems are one of the most remarkable structures elucidated in 20th century mathematics. They have a simple definition in terms of linear algebra and combinatorics, but have...

Honours Project Dr Masoud Kamgarpour
Representation theory of infinite-dimensional Lie algebras

Conformal field theory plays a fundamental role in string theory and in the description of phase transitions in statistical mechanics. The basic symmetries of a conformal field theory are generated by infinite-dimensional Lie...

PhD Project
Masters Project
Dr Jorgen Rasmussen
Hitchin's fibration and its application in mathematics and physics

Defined by the eminant mathematical physics Nigel Hitchin, the Hitchin's...

PhD Project Dr Masoud Kamgarpour
Representations of jet Lie algebras

Representations of semisimple Lie algebras is one of the most beautiful parts of mathematics in the 20th century. It draws on...

Masters Project Dr Masoud Kamgarpour
Game theory and algebraic geometry

Nash's equilibrium is a celebrated result in mathematics and economics. It is one of the foundational results in game theory. The aim of this project is to explore the relationship between game theory and algebraic geometry. 

Honours Project Dr Masoud Kamgarpour