Student Number Theory Seminar

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:

• Room: MC 5403
• Zoom link: https://uwaterloo.zoom.us/j/98347327227?pwd=anFGNjRsd0ZPUk10SW9vQVNqL3Z0UT09