First lecture: Topology of subvarieties of semi-abelian varieties

Abstract: Many smooth quasi-projective varieties, such as higher genus curves and essential hyperplane arrangement complement, can be embedded into semi-abelian varieties. It is known that such varieties have nonnegative signed Euler characteristics, i.e., $(-1)^{\dim X}\chi(X)\geq 0$. I will discuss two perspectives of this result via the index theorem and the generic vanishing theorem. I will also talk about a recent Morse theoretic proof, which is joint work with Yongqiang Liu and Laurentiu Maxim.

Second and third lectures: Perverse sheaves on semi-abelian varieties and Mellin transformation

Abstract: Mellin transformation is the constructible sheaf analog of Fourier-Mukai transformation. It is very useful to study the cohomological properties of constructible complexes on semi-abelian varieties. We will discuss a characterization of perverse sheaves on semi-abelian varieties using Mellin transformation, which generalizes Schnell's result for abelian varieties and Gabber-Loeser's result for affine tori. This is also joint work with Yongqiang Liu and Laurentiu Maxim.