Decoupling for Cantor Sets

In this talk we discuss sharp ℓ2L2n estimates for Cantor sets. These estimates are related to the work of Biggs bounding the number of solutions to a certain type of Diophantine equations for integers contained in Ellipsephic sets, sets of numbers missing certain digits in base p. We discuss the connection between both problems, and exploit it to find computational methods to find sharp decoupling estimates. Joint work with A. Chang, R. Greenfeld, A. Jamneshan, Z.K. Li and J. Madrid.