The course will begin with a quick review of some topics already covered during the fall, including the proofs of some theorems presented then. After that, the course will focus on advanced topics, centered around the use of PDEs in Riemannian geometry. Possible topics include fundamental results on elliptic and parabolic PDEs on a Riemannian manifold, the Hodge theorem, the Ricci flow, isoperimetric and Sobolev inequalities.
Lecture  Date  Topics 

1  2/7/2018 

2  2/14/2018 

3  2/21/2018 

4  2/28/2018  Guest lecture by Matt Grayson 
5  3/7/2018 

3/14/2018  Spring Recess  
6  3/21/2018 

7  3/28/2018 

8  4/4/2018 

9  4/11/2018  TBA 
10  4/18/2018  TBA 
11  4/25/2018  TBA 
12  5/2/2018  TBA 