Title: Cohomological splitting of fibrations over rationally connected basesAbstract: A classical result of Blanchard and Deligne asserts that the rational cohomology of a smooth projective fibration splits additively. In this talk, I will discuss how to prove an analogous result for cohomology with coefficients in fields of positive characteristics. Although the splitting in this setting does not […]

Title: Curves on Varieties and the Degree of Irrationality.Abstract: Inspired by the Noether-Lefschetz theorem, it has been conjectured that the degree of any curve on a (very) general complete intersection variety is divisible by the degree of the variety itself. In this talk, we present a weaker version of this conjecture. Using this result, we confirm a […]

Title: Twisted Intermediate Jacobian Fibrations.Abstract:In this talk, I will report on a joint work in progress with D. Mattei and E. Shinder, where we construct, using Hodge modules, a group scheme that can be thought of as the intermediate Jacobian of a certain complete family of cubic threefolds. We show that the group scheme acts on […]