Computational Algebra Seminar

Derek Holt
(University of Warwick, UK)
On Coxeter's Families of Group Presentations
3pm–4pm, Tuesday 27th October, 2009
Carlaw 535
In 1939, Coxeter first studied the family of groups defined by the presentations:
(l,m,n;q) = < r,s | r^l, s^m, (rs)ⁿ, [r,s]^q > .
Until recently, the finiteness of only 6 of these groups remained undecided:
(2,3,13;4), (3,4,9;2), (3,4,11;2), (3,4,13;2), (3,5,6;2) and (3,5,7;2).
We discuss a recent computational proof, carried out largely in Magma, by George Havas and myself that (2,3,13;4) is finite, and that (3,4,13;2) and (3,5,7;2) are infinite.

Daniel J. Bernstein
(University of Illinois at Chicago)
Speeding up characteristic 2
4pm–5pm, Tuesday 27th October, 2009
Carlaw 535
This talk will describe some recent advances in software speed for various computations in fields of characteristic 2. This talk will explain, for example, why the latest speed records for elliptic-curve cryptography use fields of characteristic 2, and why normal bases are being used instead of polynomial bases in software to attack the "infeasible" ECC2K-130 challenge.