Joel Sievert : A Quick Review of Hodge Theory

Posted by Paul Reschke , part of the Graduate Student Colloquium.

At

Nov. 26, 2012, 4:15 p.m.

In

SEO 636

Abstract

In this talk we'll be examining the Hodge structure of smooth, compact complex Kahler manifolds (or complex projective algebraic varieties). We'll be concerned primarily with surfaces, but most of the information will be applicable in general dimension. Roughly, Hodge theory is the study of differential forms on a smooth manifold. Our primary goal will be to recall the Hodge Index Theorem and the Lefschetz Theorem on (1,1)-classes. This talk is intended to be accessible to graduate students of all levels; no technical knowledge of Hodge theory will be expected.