**R. Parimala**

Emory University, USA

August 14, 2012

**Period-index problem for the Brauer group**:
Class field theory leads to period=index for finite dimensional
division algebras over number fields. There are open questions concerning bounding the index of algebras in terms of their period
for fields finitely generated fields over prime fields. We shall explain how such bounds would lead to nontrivial consequences for the existence of rational points on quadrics.