Available Projects
| 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 |
