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【北航数学论坛】_12月23日李洪波教授报告
ag平台网址:2016-12-19  浏览量:

From Basis-Free Solutions of Quaternionic Equations to Basis-Free Symbolic Manipulations of Quaternionic Polynomials

李洪波教授报告时间:2016年12月23日(周五)上午10:30-11:30报告地点:北航数学与系统科学ag平台app下载主213学术交流厅Abstract:

Quaternions are a basic algebraic tool in mathematics, and have important applications in geometry and geometry-related theoretical and engineering problems. A quaternionic variable is of the form q=u+xi+yj+zk, where u,x,y,z are scalar variables and i,j,k are a basis of the vector part of q, and q itself is called the basis-free form of the quaternionic variable. A quaternionic polynomial is a linear combination of quaternionic products of sequences of quaternionic parameters and quaternionic variables, where the products are associative but non-commutative. The problem of finding basis-free solutions of quaternionic polynomial equations dates back to the 1880's in the work of Sylvester. Finding the basis-free solution of a general linear quaternionic equation has been a problem unsolved since then. We solved the problem recently. We further consider the problem of rigorous definition of basis-free quaternionic polynomial ring for the purpose of basis-free symbolic manipulations with certified theoretical completeness. We also solved the problem recently. This talk presents our recent progress on the two problems.

报告人概况:

李洪波教授,中科院数学与系统科学研究院研究员,现为中科院数学机械化重点实验室主任。1997年入选中科院中科院“百人计划”;1998年获香港“求是杰出青年学者”奖;1999年获德国洪堡基金会德国洪堡研究基金; 2001年获国务院政府特殊津贴, 2001年国家人事部中国(十大)优秀博士后;2004年获中科院数ag平台app下载突出成果奖和国家人事部百千万人才工程首批国家级人选。2009年,获“国家杰出青年基金”。研究主要领域有自动几何推理,几何计算,Clifford代数及其在计算机视觉和机器人方面的应用。李洪波教授主创的共形几何代数,已经成为国际几何代数研究的主流,它的应用前景非常广阔。

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