IISER Pune
INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

The history of matrix positivity preservers 
 
Mon, Oct 16, 2017,   04:00 PM to 05:00 PM at Madhava Hall

Dr.Apoorva Khare
IISc Bangalore

I will give a gentle historical (and ongoing) account of matrix positivity
and of operations that preserve it. This is a classical question studied
for much of the past century, including by Schur, Polya-Szego, Schoenberg,
Kahane, Loewner, and Rudin. It continues to be pursued actively, for both
theoretical reasons as well as applications to high-dimensional covariance
estimation. I will end with some recent joint work with Terence Tao
(UCLA).
 
The entire talk should be accessible given a basic understanding of linear
algebra/matrices and one-variable calculus. That said, I will occasionally
insert technical details for the more advanced audience. For example: this
journey connects many seemingly distant mathematical topics, from Schur
(products and complements), to spheres and Gram matrices, to Toeplitz and
Hankel matrices, to rank one updates and Rayleigh quotients, to
Cauchy-Binet and Jacobi-Trudi identities, back full circle to Schur
(polynomials).

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