### Products of degenerate quadratic forms, by Paul Balmer

We challenge the classical belief that products of degenerate
quadratic forms must remain degenerate and we show that this fails in
general, e.g. over tensor triangulated categories with duality. This
opens new ways of constructing non-degenerate quadratic forms and
hence classes in Witt groups. In addition, we encapsulate in a
Leibniz-type formula the behaviour of the product with respect to the
symmetric cone construction. We illustrate these ideas by computing
the total Witt group of regular projective spaces.

Paul Balmer <balmer@math.ethz.ch>