Nikhil Srivastava, an Indian computer scientist and math genius has solved a 62-year-old quantum physics problem with his team and won a top US prize. He worked with his two friends Daniel Spielman (Sterling Professor of Computer Science, a professor of statistics and data science, and a professor of mathematics) and Adam Marcus (the Chair of Combinatorial Analysis at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland). It took him 5 years to find out the solution to the Kadison-Singer problem which arose in 1959 and remained unsolved for 62 years.
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He has been jointly selected for the inaugural Ciprian Foias Prize in Operator Theory by American Mathematical Society (AMS). He shared a joint statement with other awardees that they would accept this award on behalf of people who contributed to the resolution of this problem.
This is not his first award. In 2014, he has won the George Polya Prize, Michael and Shiela Held Prize in 2021 and Ciprian Foias Prize is his third award.
The Ciprian Prize was created in 2020 in the memory of an influential scholar, Ciprian Foias. It will be presented in January 2022 and current prize amount is US$ 5,000. It will be presented at the largest mathematicians gathering in the world at 2022 Joint Mathematics Meeting in Seattle.
They are getting award for their “highly original work”. They used certain methods including iterative sparsification and interlacing polynomials to find out the solution. Their ideas offered a tool kit that can be used for many future applications.
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Many people could not find out the solution for last 50+ yeas and that is why they are getting this award. They also published new constructions of Ramanujan graphs that described interconnected data networks which revealed a new link between graph theory, linear algebra and polynomials.
The 1959 Kadison-Singer Problem
In mathematics, the Kadison–Singer problem, posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals on certain C*-algebras were unique. The uniqueness was proven in 2013.
The statement arose from work on the foundations of quantum mechanics done by Paul Dirac in the 1940s and was formalized in 1959 by Richard Kadison and Isadore Singer. The problem was subsequently shown to be equivalent to numerous open problems in pure mathematics, applied mathematics, engineering and computer science.
Kadison, Singer, and most later authors believed the statement to be false, but, in 2013, it was proven true by Adam Marcus, Daniel Spielman and Nikhil Srivastava, who received the 2014 Pólya Prize for the achievement.
The solution was made possible by a reformulation provided by Joel Anderson, who showed in 1979 that his “paving conjecture”, which only involves operators on finite-dimensional Hilbert spaces, is equivalent to the Kadison–Singer problem. Nik Weaver provided another reformulation in a finite-dimensional setting, and this version was proved true using random polynomials.
The original problem was as follows:
If one had to know about the state of a quantum system, would having complete knowledge of its sub systems help understand this system? If yes, to what extent?
This resembles the practical concept of matrices. The above problem is equivalent to the following question:
Could matrices be broken down into more depth and simplified? If yes, how much?
This problem utilises knowledge of various fields, like maths, engineering and quantum physics.
Who is Nikhil Srivastava – the Indian Maths Genius
Nikhil Srivastava is an associate professor of Mathematics at University of California, Berkeley. In July 2014, he was named a recipient of the Pólya Prize with Adam Marcus and Daniel Spielman.
He was born New Delhi, India and attended Union College in Schenectady, New York, graduating summa cum laude with a bachelor of science degree in mathematics and computer science in 2005. He received a PhD in computer science from Yale University in 2010 (his dissertation was called “Spectral Sparsification and Restricted Invertibility”).
Together with Adam Marcus and Daniel Spielman, he provided a positive solution to the Kadison–Singer problem, a result that was awarded the 2014 Pólya Prize.
He gave an invited lecture at the International Congress of Mathematicians in 2014. He jointly won the 2021 Michael and Sheila Held Prize along with two others for solving long-standing questions on the Kadison-Singer problem and on Ramanujan graphs.