Luis Felipe Tabera: Multiple points, tropical Severi varieties and the Casas Alvero conjecture

Abstract: A Casas Alvero polynomial is a complex univariate polynomial f such that for every derivative fi, f and fi share a common root. Casas Alvero conjecture states that the only Casas Alvero polynomials are of the form \(a(x-b)^n\).
 
In this talk, We will recall some results obtained with A. Dickenstein and M.I. Herrero about tropical Severi varieties and multiple roots. We apply these techniques to study tropicalizations of Casas Alvero polynomials. We will provide an upper bound on the dimension of the algebraic set of Casas Alvero polynomials without recycled roots.