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October 20, 2015

Talk of Prof. Mihai Putinar

--- Title: Matrix positivity preservers in fixed dimension

Time
October 20, 2015

Prof. Mihai Putinar
Department of Mathematics
University of California, Santa Barbara, USA

 

Tuesday 2015-10-20 16:00
IST-Seminar-Room V2.268 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen

 

Abstract

A celebrated 1942 result of Schoenberg characterizes all entry-wise functions which preserve positivity of matrices of any size. Roger Horn PhD dissertation (late 60-ies) improved the result by obtaining necessary conditions on a polynomial to preserve positivity on matrices of a fixed size. I will present a characterization of polynomials which preserve positivity when applied entry-wise on matrices of a fixed dimension. All put in historical context and motivated by recent demands of statistics of large data and optimization theory. A sketch of the proof will take a detour through the representation theory of the symmetric group. Joint work with Alexander Belton, Dominique Guillot and Apoorva Khare.

Biographical Information

Educated at the University of Bucharest, and working at the Research Institute of Mathematics of the Romanian Academy of Sciences until 1990. Since 1990 Professor at the University of California (first Riverside, until 1997, then Santa Barbara). Also Professor of Mathematics at the University of Newcastle (UK). Visiting Professor positions at a dozen institutions in Europe, America and Asia. Over 150 research articles, a dozen books (edited or authored). Working in the fields of Operator Theory, Function Theory of a Single or Several Complex Variables, Approximation Theory. Order of Merit of the Romanian State, with the rank of Knight.

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