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SUMMARY:Modern applications of classical number theory - Cong Ling (Imperi
 al College London)
DTSTART:20191106T134500Z
DTEND:20191106T144500Z
UID:TALK131809@talks.cam.ac.uk
CONTACT:Peter Varju
DESCRIPTION:Number theory has been a subject of pure mathematics for a lon
 g period of time. One big change in recent decades is that it has become a
 n applied subject\, driven by numerous applications to modern information 
 technology. This talk will highlight some new applications of number theor
 y\, especially lattices and algebraic number theory\, to the design of cap
 acity-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 wi
 th coefficients 0\, +1\, -1. The other is concerned with beta-expansion (o
 r Bernoulli convolution) for the design of polar codes in the upcoming 5G 
 mobile networks.
LOCATION:MR5\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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