Title:On Atiyah's linear independence conjecture for four points in a hyperbolic plane

Abstract:Atiyah proposed his linear independence conjecture in about 2000 aiming at a solution to a problem in physics. Given n distinct points in a Euclidean space, a set of n-1 unit vectors is naturally associated to each of the given points, and, regarding each unit vector as a complex number via the stereographic projection, one obtains a monic polynomial of degree n-1 having as roots the n-1 complex numbers corresponding to the unit vectors. The conjecture asserts that the set of n polynomials so obtained is linearly independent. There is a similar conjecture for points in a hyperbolic space. The conjecture has been proved for the case of four points in a Euclidean space, and the case of four points in a hyperbolic space which do not lie in a hyperbolic plane. In joint work with Jiming Ma, we confirm Atiyah's independence conjecture for the case of four points in a hyperbolic plane.

报 告 人：张影 教授 苏州大学 数学科学学院

报告时间：2016年12月22日（星期四）下午16：30~17：30

报告地点：数学科学学院38号楼报告厅

主办单位：数学科学学院

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