Colloquium: Galbraith -- Linear Algebra with Errors, Coding Theory, Cryptography and Fourier Analysis on Finite Groups

Solving systems of linear equations Ax=b is easy, but how can we solve such a system
when given a "noisy" version of b? Over the reals one can use the least squares method,
but the problem is harder when working over a finite field.  Recently this subject has
become very important in cryptography, due to the introduction of new cryptosystems with
interesting properties.  

The talk will survey work in this area.  I will discuss connections with coding theory
and cryptography.  I will also explain how Fourier analysis in finite groups can be used
to solve variants of this problem, and will briefly describe some other applications of
Fourier analysis in cryptography.  The talk will be accessible to a general mathematical
audience.