AsianScientist (Jul 15, 2014) – Nikhil Srivastava, a researcher at Microsoft Research India, along with colleagues Adam Marcus and Daniel A. Spielman of Yale University, has won the 2014 George Pólya Prize for solving a 50 year old mathematical problem, the Kadison-Singer conjecture.
The Kadison-Singer conjecture is a question about the mathematical foundations of quantum mechanics first proposed in 1959 by the mathematicians Richard Kadison and Isadore Singer.
“Nikhil Srivastava and his co-authors have settled an important, 54-year-old problem in mathematics,” said Ravi Kannan, principal researcher in the Algorithms Research Group at Microsoft Research India. “They gave an elegant proof of a conjecture that has implications for many areas of mathematics, computer science, and quantum physics.”
Srivastava offers a layman’s explanation of what he, Marcus and Spielman have achieved.
“We proved a very fundamental and general statement about quadratic polynomials that was conjectured by [mathematician] Nik Weaver that implies Kadison-Singer. The proof is based on a new technique we developed, which we call the ‘method of interlacing families of polynomials.’
“My main reaction was awe at how beautiful the final proof was,” he recalls. “I actually started laughing when I realized that it worked. It fit together so beautifully and sensibly you knew it was the ‘right’ proof and not something ad hoc. It combined bits of ideas that we had generated from all over the five years we spent working on this.”
Settling the Kadison-Singer conjecture shows an important way in which experiments are enough to provide a complete description of a quantum system.
“It has clear implications for the foundations of quantum physics,” he says. “It implies that it is possible to ‘approximate’ a broad class of networks by networks with very few edges, which should have impact in combinatorics and algorithms. Finally, it is equivalent to several conjectures in signal processing and applied mathematics that seem to have practical use.”
Pólya (1887-1985) was a Hungarian mathematician who served as a professor for four decades, first at ETH Zurich, then at Stanford University. He is credited with fundamental advances in combinatorics, numerical analysis, number theory, and probability theory.
The Pólya Prize is presented by the Society for Industrial and Applied Mathematics every two years, alternating between two categories: notable application of combinatorial theory and notable contribution to Pólya’s areas of interest, including approximation theory, complex analysis, number theory, orthogonal polynomials, probability theory, and mathematical discovery and learning.
The article can be found at: Marcus et al. (2014) Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem.
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Source: Inside Microsoft Research.
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