Special Session:
Computational Algebra

Organizers: Eamonn O'Brien (Auckland) and Götz Pfeiffer (NUI, Galway)

Tuesday, April 7 2009

14:15 - 15:10    Kirwan Lecture Theatre

Dane Flannery (NUI Galway):
On deciding finiteness of matrix groups

We describe practical algorithms for deciding finiteness and computing orders of matrix groups defined over any infinite field. This is joint work with Alla Detinko.

15:15 - 16:10    Kirwan Lecture Theatre

Gunter Malle (Kaiserslautern):
Computing in Hecke algebras

Hecke algebras are deformations of group algebras of reflection groups. They play a crucial role in the representation theory of finite groups of Lie type. In the talk we report on various methods for the construction of irreducible representations of Hecke algebras and show how the explicit models of representations can be used to derive structural properties.

16:30 - 17:25    Kirwan Lecture Theatre

Arjeh Cohen (Eindhoven):
Constructions of curves with given groups of automorphisms

We describe how we found smooth curves of prescribed genus and with a prescribed group of automorphisms. We also show some pictures of these curves.

Wednesday, April 8 2009

14:15 - 15:10    Kirwan Lecture Theatre

Steven Galbraith (Royal Holloway University of London):
Elliptic curves and public key cryptography

Public key cryptography relies on hard computational problems in mathematics. An important example is the discrete logarithm problem (namely, given g, h in G to compute x, if it exists, such that h=g^x) in the group of points of an elliptic curve over a finite field. This talk will give a survey of elliptic curves in public key cryptography.

15:15 - 16:10    Kirwan Lecture Theatre

Gary McGuire (University College Dublin):
Some computational algebra in cryptography

We will discuss two different uses of computational algebra in cryptography. The first considers functions that can be used in substitution boxes, known as APN functions, and their equivalence. Determining equivalence can be a difficult and interesting challenge, requiring new invariants to be computed. The second problem comes from hyperelliptic curve cryptography, and the construction of suitable genus 2 curves for use in cryptography.

16:30 - 17:25    Kirwan Lecture Theatre

Bettina Eick (Braunschweig):
Isomorphism testing for algebras (Lie or associative)

We describe an algorithm to solve the isomorphism problem for algebras defined over finite fields. The algorithm has three cases: nilpotent algebras, solvable algebras and arbitrary (in particular simple) algebras. Applications of the algorithm include: checking the modular isomorphism problem for p-groups and constructing new simple Lie algebras in characteristic 2.