**Instructor:** Bill Minicozzi

**Email:** minicozz [at] math . mit .edu

**Office:** Room 2-371

**Lectures:** TR 9:30 - 11 2-135

## COURSE DESCRIPTION

Differential forms, introduction to Lie groups, the DeRham theorem, Riemannian manifolds, curvature, the Hodge theory. 18.966 is a continuation of 18.965 and focuses more deeply on various aspects of the geometry of manifolds. Contents vary from year to year, and can range from Riemannian geometry (curvature, holonomy) to symplectic geometry, complex geometry and Hodge-Kahler theory, or smooth manifold topology. Prior exposure to calculus on manifolds, as in 18.952, recommended.

**Prerequisites:** 18.101, 18.950 or 18.952

**Text Book:** Riemannian Geometry, do Carmo.