Asymptotically-fast algorithms for polynomial and matrix problems generally reduce to fast multiplication. I will show how this can be implemented very effectively, in practice, in a variety of situations. In particular, the Brent-Kung modular composition algorithm can be implemented to apply fast algorithms for both polynomial and matrix multiplication in a nice way.
Tutorial style talk demonstrating how to work with curves in Magma. The examples will be mainly related to cryptography but there may be some other wacky stuff.