Bing Wang, Spring 2018:
Bing Wang, Spring 2018: Topics include: Fourier Transform and Sobolev spaces, Laplace operator on a Riemannian manifold, Weak maximum principle,
the heat kernel on a manifold, spectral properties, Gaussian estimates, Green function, Ultracontractive estimates and eigenvalues, bundle valued heat kernel.
. Heat kernel and Analysis on Manifolds, Alexander Grigor'yan.
. Heat kernels and spectral theory, E.B. Davies.
Jeff Viaclovsky (Fall 2017):
This course will cover various advanced topics in Differential Geometry. Topics will be selected from the following.
(1) Asymptotic expansions of metric, volume, etc.
(2) Curvature decomposition and representation theory.
(3) Complex manifolds and Kaehler metrics.
(4) Hodge Theory and Fredholm Theory on compact Riemannian manifolds.
(5) Analysis on noncompact Riemannian manifolds.