Three Lectures on the Topology of Semi-abelian Varieties

2018-08-13 10:00 - 2018-08-17 11:30 Room 78201, Jingchunyuan 78, BICMR

\n\tTime: 8\/13, 8\/15, 8\/17, 10:00 - 11:30<\/span>\n<\/p>\n



\n\t\tFirst lecture: Topology of subvarieties of semi-abelian varieties\n\t<\/div>\n\t
\n\t\tAbstract: 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.\n\t<\/div>\n\t
\n\t\tSecond and third lectures: Perverse sheaves on semi-abelian varieties and Mellin transformation\n\t<\/div>\n\t
\n\t\tAbstract: 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.\n\t<\/div>\n\t