Decoupling and discrete restriction inequalities have been very fruitful in recent years to solve problems in additive combinatorics and analytic number theory. In this talk I will present some work in decoupling for Cantor sets, including Cantor sets on a parabola, decoupling for product sets, and give applications of these results to additive combinatorics. Time permitting, I will present some open problems.

Contains joint work with Alan Chang, Rachel Greenfeld, Paata Ivanisvili, Asgar Jamneshan, Zane Li and José Ramón Madrid Padilla