Owen Sharpe, Department of Pure Mathematics, University of Waterloo
"Vinogradov's Mean Value Theorem and Bourgain's Discrete Restriction Conjecture"
Vinogradov's Mean Value Theorem is a long-standing conjecture, about the asymptotics of the number of solutions to a particular system of Diophantine equations, which was recently resolved by Wooley, Bourgain, Demeter, and Guth. Bourgain made an additional conjecture about a related Diophantine system, which was proven very recently for most cases by Hughes and Wooley. We discuss the Diophantine techniques used in the theorems and give a proof sketch of the latter.
This seminar will be held both online and in person: