报告题目：Hurwitz problem on quadratic forms and composition algebras

报 告 人：Maxim Goncharov

所在单位：Sobolev Institute of Mathematics

报告时间：November 12, 10:30-11:30

报告地点：禁漫天堂 数学楼第五研讨室

报告摘要: 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).

报告人简介： Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.