The Hong Kong Polytechnic University
Title：Minimal Integrity Bases of Invariants of Second Order Tensors in a Flat Riemannian Space
Liqun Qi is now Professor of Applied Mathematics and Head of Department of Applied Mathematics at The Hong Kong Polytechnic University. Professor Qi has published more than 200 research papers in international journals. He established the superlinear and quadratic convergence theory of the semismooth Newton method, and played a principal role in the development of reformulation methods in optimization. Professor Qi’s research work has been cited by the researchers around the world. According to the authoritative citation database www.isihighlycited.com, he is one of the world’s most highly cited 300 mathematicians. In 2005,Professor Qi pioneered the research on eigenvalues for higher order tensors, which now has applications in biomedical engineering, statistical data analysis, spectral hypergraph theory, solid mechanics, etc. In 2010, Professor Qi received the First Class Science and Technology Award of Chinese Operations Research Society
Abstract：In this talk, we study invariants of second order tensors in an n-dimensional flat Riemannian space. We define eigenvalues, eigenvectors and characteristic polynomials for second order tensors in such an n-dimensional Riemannian space and show that the coefficients of the characteristic polynomials are real polynomial invariants of that tensor. Then we give minimal integrity bases for second order symmetric and antisymmetric tensors, respectively, and study their special cases in the Minkowski space and applications in electrodynamics, etc.