Xiaomei Zhao, Pure Mathematics, University of Waterloo
"New strategies for minor arc estimates: Part II"
Abstract: We have seen the outline of the circle method in Waring's problem from Shuntaro's talks, where the minor arc contribution was established by combining Weyl's inequality with Hua's lemma. In my two talks, we will continue to see some improvements on minor arc estimates. The first method is to replace Hua's lemma by Vinogradov's mean value theorem (VMVT). The second method is Wooley's recent strategy for transforming VMVT to minor arc estimates. If time allows, we may sketch Ford's method as well.