Phillip Griffiths, National Academy of Sciences: Positivity in Hodge theory & algebraic geometry 2

Positivity in Hodge Theory with Applications to Algebraic Geometry
presented by
Professor Phillip Griffiths
Arts and Sciences Distinguished Scholar
University of Miami
Ungar Building, Room 528B
Wednesday, November 13, 2024, 11:30am
Thursday, November 14, 2024, 3:00pm
Abstract: The Hodge-Riemann bilinear relations define metrics in the vector bundles associated to a family of polarized Hodge structures. These metrics have associated curvatures that have very interesting geometric and analytic properties. These properties suggest, and in many cases lead to proofs, of many deep results concerning the variation of the cohomology of the fibers in families of algebraic varieties.
In these two lectures we will discuss these results from the perspective of the global differential geometry of period mappings.