Khovanov homology and positivity notions

In this talk, we discuss what 'positivity' means in the study of links. We will examine several notions of positivity and explore how different versions of Khovanov homology—such as even, odd, and HOMFLY–PT homologies—can be used to study them. These homological techniques provide powerful methods for uncovering the structural and geometric properties of positive links. This talk is based mainly on joint work with M. Kegel, L. Mousseau, and M. Silvero.