Title Project Discription Level Supervisor
KLR algebras/categorified quantum groups

In 2008, Khovanov and Lauda introduced a remarkable family of algebras designed for the...

PhD Project
Masters Project
Dr Peter McNamara
Spherical Functions

A classical result due to MacDonald shows that certain functions (so-called spherical functions) that appear in representation theory of p-adic groups are well known symmetric functions. This project will study this theorem of MacDonald,...

Masters Project
Honours Project
Dr Peter McNamara
Computing with Quantum Groups

Quantum groups are remarkable q-analogues of the theory of Lie groups and Lie algebras introduced by Jimbo and...

Masters Project
Honours Project
Summer Project
Dr Peter McNamara
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
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
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
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
Associate Professor Jorgen Rasmussen
Diagram algebras and integrable lattice models

Diagram algebras offer an intriguing mathematical environment where computations are performed by diagrammatic manipulations. Applications include knot theory and lattice...

PhD Project
Masters Project
Honours Project
Associate Professor Jorgen Rasmussen
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
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
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
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
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
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
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