Grothendieck-Witt groups of quadrics and sums-of-squares formulas

This thesis studies Grothendieck-Witt spectra of quadric hypersurfaces. In particular, we compute Witt groups of quadrics. Besides, by calculating Grothendieck-Witt groups of a deleted quadric over an algebraically closed field of characteristic different from 2, we improve Dugger and Isaksen’s condition (some powers of 2 dividing some binomial coefficients) on an old problem Hurwitz concerning the existence of sums-of-squares formulas