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Modern applications of classical number theory

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If you have a question about this talk, please contact Peter Varju.

Number theory has been a subject of pure mathematics for a long period of time. One big change in recent decades is that it has become an applied subject, driven by numerous applications to modern information technology. This talk will highlight some new applications of number theory, especially lattices and algebraic number theory, to the design of capacity-achieving codes for wireless communications and to the construction of cryptosystems with resilience against quantum attacks (aka post-quantum cryptography). Two open problems will be presented, which are hopefully interesting to number theorists. One problem lies at the foundation of the NTRU cryptosystem, which involves the ratio of two random polynomials with coefficients 0, +1, -1. The other is concerned with beta-expansion (or Bernoulli convolution) for the design of polar codes in the upcoming 5G mobile networks.

This talk is part of the Discrete Analysis Seminar series.

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