Title: Quadratic forms and a local-global principle. (joint with Julia Hartmann and Daniel Krashen) Abstract: Patching methods, which have been used to prove results about etale fundamental groups, can be used to obtain a local-global principle for the existence of F-rational points on homogeneous spaces, where F is the function field of a curve over a discretely valued field. This in turn yields local-global principles for quadratic forms and for central simple algebras; for quadratic forms, the precise statements of these local-global principles depend on the fundamental group of the graph associated to the closed fiber of a model of the curve. Using these local-global principles, results can be obtained over function fields regarding the u-invariant (concerning dimensions of anisotropic quadratic forms) and the period-index problem for the Brauer group.