Dr Victor Scharaschkin
Lecturer, Honours Co-ordinator
|Computational number theory||
There is also scope for work in computational number theory such as primality testing and factorization methods
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...
|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...
|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)....