Algebraic boundaries among typical ranks for real binary forms

Binary real forms of degree d admit as typical ranks all the integers between floor(d/2)+1 and d. We investigate the boundary between the open subset of rank r forms and the open subset of rank r+1. These boundaries are known only in the extreme cases, by Lee-Sturmfels (between rank floor(d/2)+1 and floor(d/2)+2) and Comon-Ottaviani (between rank d-1 and d). We investigate the intermediate boundaries. In the talk I will present our new results, focusing on the case of degree 7 forms. This is work in progress with G.Stagliano'.