On the Waring rank of binary forms: The binomial formula and a dihedral cover of rank two forms

Waring problem for forms, which dates back to J.J. Sylvester, has demonstrated to be a fruitful and enriching problem in algebraic geometry, which have found recently wide applications in biology, signal processing, machine learning, quantum information theory... In this talk, we will start overviewing Waring type problems, emphasizing applications.

Thereafter, we will review a couple of results obtained in joint work with Shreedevi K. Masuti for binary forms with complex coefficients. The most remarkable of our results is an explicit formula for the Waring rank of any binomial.