I will discuss a recent paper of mine, the aim of which is to count the number of prime solutions to Q(p1,..,p8) = N, for a fixed quadratic form Q and varying N. The traditional approach to problems of this type, the Hardy-Littlewood circle method, does not quite suffice. The main new idea is to involve the Weil representation of the symplectic groups Sp8(ℤ/qℤ). I will explain what this is, and what it has to do with the original problem. I hope to make the talk accessible to a fairly general audience.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
