Topic: Tensors and entanglement in quantum physics

Lecturer: Porf. Shmuel Friedland 

Time：14：00 -15:00, Thursday, May 26, 2016

Place：Room 321, Main Building

Abstract： Tensor, or multiarrays with $dge 3$ indices, are ubiquitous in modern applications, mainly due to data explosion. While matrices, $d=2$, are well understood and widely used, tensors pose theoretical and numerical challenges. Tensors also arise naturally in quantum physics, when dealing with $d$-particle systems. In this talk, for general mathematical audience, we will describe several fundamental results and problems in tensors: tensor ranks, low rank approximation of tensors, spectral and nuclear norm of tensors, and their relation to the entanglement and nonseparability in quantum information theory.

Biographer：

He received all his degrees in Mathematics from Israel Institute of Technology,(IIT), Haifa, Israel: B.Sc in 1967, M.Sc. in 1969, D.Sc. in 1971. He held Postdoc positions in Weizmann Institute of Science, Israel; Stanford University; IAS, Princeton. From 1975 to 1985, he was a member of Institute of Mathematics, Hebrew U., Jerusalem, and was promoted to the rank of Professor in 1982. Since 1985 he is a Professor at University of Illinois at Chicago. He was a visiting Professor in University of Wisconsin; Madison; IMA, Minneapolis; IHES, Bures-sur-Yvette; IIT, Haifa; Berlin Mathematical School, Berlin. Friedland contributed to the following fields of mathematics: one complex variable, matrix and operator theory, numerical linear algebra, combinatorics, ergodic theory and dynamical systems, mathematical physics, mathematical biology, algebraic geometry. He authored one book and about 200 papers, with many known coauthors, including one Fields Medal winner. He received the first Hans Schneider prize in Linear Algebra, jointly with M. Fiedler and I. Gohberg, in 1993. He was awarded recently a smoked salmon for solving the set-theoretic version of the salmon problem: http://www.dms.uaf.edu/~eallman. For more details on Friedland vita and research, see http://www.math.uic.edu/~friedlan.