Beijing Institute of Mathematical Sciences and Applications

Quadratic forms over a field is an old topic in mathematics, which really began with the pioneering work of Witt. The essential object to study is the Witt group, which is built by extensions of etale cohomology (Fields medal). It was Knebusch and Balmer who generalized the idea to algebraic varieties. To compute the Witt group, the Gersten-Witt spectral sequence is a powerful tool for low dimensional algebraic varieties. It was shown by Knebusch, Sujatha and Mahe that the free rank of Witt group of real algebraic varieties is equal to the number of Euclidean connected components of real points. The computation of Witt group of Grassmannian varieties by Balmer and Calmes initiated an enumerative geometry resulting in a quadratic form.