Report Title：Hurwitz problem on quadratic forms and composition algebras

Reporter：Maxim Goncharov

Affiliated unit：Sobolev Institute of Mathematics

Report time：November 12, 10:30-12:30

Report location：Fifth Discussion Room, Mathematics Building, Jilin University

Report Abstract: The original Hurwitz problem may be formulated as: given a natural number n and two sets of numbers x_1,...,x_n and y_1,...,y_n from a field F, is it possible to find elements z_1,...z_n from F such that

(x_1^2+x_2^2+...+x_n^2)(y_1^2+y_2^2+...y_n^2)=z_1^2+z_2^2+...+z_n^2?

For n=2, the positive solution of this question follows from the property of the module of complex numbers. In this talk, we will consider this problem in detail. Also, we will consider additional structures that appeared naturally while solving this problem (such as alternative and composition algebras, quaternions, and octonions).

Presenter Introduction： Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.