Mathematical sciences seminar: From Harmonic Analysis through Poincare Conjecture to Matrix Determinant



Fuzhen Zhang
Nova Southeastern University, Florida, USA


With a brief survey on the Harnack inequalities in various forms in Functional Analysis, in Partial Differential Equations, and in Perelman’s solution of the Poincare Conjecture, we discuss the Harnack inequality in Linear Algebra and Matrix Analysis. We present an extension of Tung’s inequality of Harnack type and study the equality case. This is a joint work with Minghua Lin.

Speaker's Bio

Fuzhen Zhang received his Ph.D. from University of California-Santa Barbara (UCSB) in 1993. He is currently a professor of Nova Southeastern University in Fort Lauderdale, Florida, USA.

Zhang’s research interests include matrix analysis, linear and multilinear algebra, functional analysis, operator theory, and combinatorics. He has published approximately 130 math-related items, including 70 research articles and three books: Linear Algebra: Challenging Problems for Students (Johns Hopkins University Press), Matrix Theory (Springer), and editor of The Schur Complement and Its Applications (Springer).

Zhang has served on the editorial boards of several mathematical journals. He has given 80 talks on mathematics worldwide, including the plenary talk at the 2016 conference on Recent Advances in Linear Algebra and Graph Theory at the University of Tennessee—Chattanooga; the plenary talk at the 18th International Linear Algebra Society (ILAS) Conference in Rhode Island in 2013; and as an invited speaker at the 22nd International Workshop on Matrices and Statistics at Fields Institute at the University of Toronto, Canada, in 2013. He has served as Chair or Co-chair of the Scientific Organizing Committee of the serial International Conference on Matrix Analysis and Applications (ICMAA). He has been a guest professor of several Chinese universities, including Shanghai University.

Zhang received the 2016 Shanghai City Overseas Renowned Professor Award. He is a recipient of the FCAS Distinguished Professor Award (2013) and NSU’s Professor of the Year award (2013). He is one of the founders of the Chinese Association of Science, Education, and Culture (CASEC, established 1994). He served as the Principal of Contemporary Chinese School of South Florida (CCSSF-Broward Campus) 2000-2002.