# Families and dichotomies in the circle method

## Location

Zoom

Wednesday, November 16, 2022 9:00 AM

Victor Wang, NYU

I will explain how one can combine algebro-geometric dichotomies and the Ratios Conjectures of Conrey, Farmer, and Zirnbauer, over a certain family of L-functions, to conditionally prove a conjectured asymptotic dichotomy, going back to Hooley and Manin, for the 6-variable cubic equation x_1^3 + ... + x_6^3 = 0 in the circle method. This is based on my thesis work under Peter Sarnak, and has statistical applications to sums of three cubes.