The continuous rank function for varieties of maximal Albanese dimension and its applications

Extended abstracts GEOMVAP 2019-geometry, topology, algebra, and applications; women in geometry and topology, 121-126, Trends Math. Res. Perspect. CRM In this note, I review an aspect of some new techniques introduced recently in collaboration with Miguel \'Angel Barja and Rita Pardini: the construction of the continuous rank function. I give a sketch of how to use this function to prove the Barja-Clifford-Pardini-Severi inequalities for varieties of maximal Albanese dimension and to obtain the classification of varieties satisfying the equalities.