Seminário de Álgebra 

18/02/2010, 15:00 — 16:00 — Sala P4.35, Pavilhão de Matemática
João Boavida, Instituto Superior Técnico

Quadratic forms and the structure of orthogonal groups

This talk will be a leisurely review of some classical material from the first two thirds of the last century, as background for the next talk (on how to actually calculate a period over $O(n\mathrm{,1})$). Specifically, today we will discuss the following topics: non-degenerate quadratic forms $Q$ over a field $k$ (for example, over $Q^3$, $Q(x)=x^2+y^2+z^2$), the parabolic subgroups of orthogonal groups $O(Q,k)$ (for the same example, $O(3)$), and the role they play on the structure of $O(Q)$. We will also see how to construct Eisenstein series over $O(Q)$.