# Hodge-Riemann Bilinear Relations and Schur Classes

# Hodge-Riemann Bilinear Relations and Schur Classes

**In-Person and Online Talk **

The classical Hodge-Riemann bilinear relations are statements about the intersection form associated to the self-wedge product of a K\"ahler form on a compact complex manifold. Gromov initiated the question as to whether there are other cohomologies that give rise to these same bilinear relations, and proved that this is the case for the intersection of (possibly different) K\"ahler classes. In this talk I will discuss joint work with Matei Toma in which we generalize this to Schur classes in various ways (for instance we prove that Schur classes of ample vector bundles as well as Schur polynomials of Kahler classes all satisfy the Hodge-Riemann bilinear relations on $H^{1,1}$). This gives rise to a number of new inequalities among characteristic classes of ample vector bundles that should be thought of as generalizations of the Khovanskii-Tessier inequalities.