Minimal surfaces have played a huge role in a wide range of areas of mathematics over the past 100 years; these include fundamental developments in geometry, topology, partial differential equations and general relativity. This course will quickly treat some of the basic material from the classical theory of two dimensional minimal surfaces in Euclidean three space. This will include the Gauss map and Weierstrass representation, the basic examples of complete minimal surfaces (e.g. catenoid, helicoid), the classical Bernstein theorem and the Douglas-Rado solution of the plateau problem. The second half of the course will treat some of the material central to the modern study of minimal hypersurfaces in Riemannian manifolds. This will include a treatment of the first and second variation formulas, stabilty results, Simons' inequality and curvature estimates for minimal surfaces.

Prerequisites: The first portion of the course will require familiarity with basic complex variables. To fully appreciate the second portion of the course some background in Riemannian geometry (at the level of Math 547) would be helpful.

References:
(1) A survey of minimal surfaces by Robert Osserman.
(2) Minimal Surfaces by Tobias Colding and William P. Minicozzi.