The existence of nontrivial zeros for quadratic forms of large dimension over the function field of a curve over a totally imaginary number field is reduced to the bounding of indices of the 2-torsion in the Brauer group of the function field. We explain how this question is related to the existence rational points on certain twisted moduli spaces of rank two stable bundles on the curve. Using this method, we explain how bounds can be established for the index in the 2-torsion of the Brauer group for alll genus 2 curves. (joint work with Jaya N. Iyer)
