Math 865 Advanced Topics in Geometry (Spring 2014)

Lectures

Recommended Textbooks/Notes

1. Elliptic Partial Differential Equations of Second Order by Gilbarg-Trudinger.
2. Einstein Manifolds by Besse.
3. 2007 Topics course lecture notes.
4. 2011 Topics course lecture notes.
5. Lectures on Riemannian Curvature Functionals, Park City Lectures in Geometric Analysis, July, 2013:
   • 1.pdf : Lecture I. Einstein-Hilbert functional, first and second variation, conformal variations, and transverse-traceless variations.
   • 2.pdf : Lecture II. Ebin-Palais slice theorem, Yamabe invariant, moduli space of Einstein metrics.
   • 3.pdf : Lecture III. Local description of moduli space of Einstein metrics, quadratic functionals, self-dual metrics.
   • 4.pdf : Lecture IV. Local minimization of quadratic functionals, B^t-flat metrics, Construction of critical points of quadratic functionals using gluing methods.

Mailing List

Selected Topics

• Elliptic theory in Holder and Sobolev spaces. Schauder Theory, L^2 theory, L^p theory.
• Theory of elliptic operators on Riemannian manifolds; Green's functions, Fredholm Theory, Hodge Theory.
• Various topics related to the Park City Lecture Notes.