A PseudoRandom InterLude on FactOrization frOm LatticeS

A PseudoRandom InterLude on FactOrization frOm LatticeS

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Katy Woo, Princeton University 

In 1935, Vinogradov introduced a method for estimating a certain class of exponential sums; as a consequence, he reduced the number of variables needed in Waring's problem and derived a new zero-free region for the zeta function. The main conjecture of Vinogradov's method, however, was not resolved until 2015 with the work of Wooley, using efficient congruencing, and Bourgain, Demeter, and Guth, using decoupling. The aim of this talk is to introduce the main ideas in the decoupling proof. In particular, we will follow the proof of Guo, Li, Yung, and Zorin-Kranich (2019) that is partially inspired by nested efficient congruencing techniques.