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Through the works of Fermat, Gauss, and Lagrange, we understand which positive integers can be represented as sums of two, three, or four squares. Hilbert’s 11th problem, from 1900, extends this questions to more general quadratic equations. While much progress has been made since its formulation, an effective solution remains out of reach. We will review some of these developments and end with some recent applications to the construction of optimally universal quantum gates in quantum computation.
Eugene Higgins Professor of Mathematics at Princeton University and permanent member at the Institute for Advanced Study, Proessor Sarnak has been awarded the Polya Price of the Society of Industrial and Applied Mathematics (1998), the Levi L. Conant Price in Number Theory (2005), and the Wolf Prize (2014). He was a member of the Stanford mathematics faculty for much of his early career, where Paul Cohen supervised his PhD. Professor Sarnak is a member of the National Academy of Sciences (USA) and Fellow of the Royal Society (UK).
You can learn more about Professor Peter Sarnak at https://www.ias.edu/scholars/sarnak