Tensor Analysis: Spectral Theory and Special Tensors

Liqun Qi

The Hong Kong Polytechnic University

16 June 2017, 2:30 pm

Abstract

Eigenvalues for tensors were introduced in 2005. Since then, a rich theory on eigenvalues of tensors and special tensors has been developed. This includes the characteristic polynomial theory, the Perron-Frobenius theory for nonnegative tensors with applications in spectral hypergraph theory and higher order Markov chains, positive semi-definite tensors and sum-of-squares tensors, completely positive tensors and copositive tensors, etc. Eigenvalues of tensors also found their applications in magnetic resonance imaging, elastic mechanics, liquid crystal study, quantum entanglement and classicality problems, etc. A book "Tensor Analysis: Spectral Theory and Special Tensors" is published by SIAM in April this year.

Bio sketch

Professor Liqun Qi received his B.S. in Computational Mathematics at Tsinghua University in 1968. his M.S, and Ph.D. degree in Computer Sciences at University of Wisconsin-Madison in 1981 and 1984 respectively. Professor Qi has taught in Tsinghua University, China, University of Wisconsin-Madison, USA, University of New South Wales, Australia, and The City University of Hong Kong. He is now Chair Professor of Applied Mathematics of Department of Applied Mathematics at The Hong Kong Polytechnic University. Professor Qi has published more than 290 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 345 mathematicians. He is ranked No. 16 in H-index among 27033 authors of Control and Optimization in the world by Microsoft Academic. Professor Qi is an editor or an associate editor of ten international journals. He has chaired more than fifteen international conferences and workshops held at Australia, Italy, Hong Kong and the Mainland China. 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, quantum mechanics, etc. He has more than110 papers on tensors, published or accepted for publication in international journals. His book "Tensor Analysis: Spectral Theory and Special Tensors," is published by SIAM in April 2017.