## Past Seminars- Differential Geometry

• Professor Tony Tromba
Tue Nov 29, 2005
4:00 pm
We will look at the history of The Theory of Branched Minimal Immersions from Jesse Douglas' solution of the Plateau Problem in 1931 ( for which he, along with Lars Ahlfors, received the first Fields Medals in 1936) to the present. We will propose a new way of looking at the theory which is, from the outset, global rather than local in nature.
• Professor Pierre van Moerbeke
Tue Nov 15, 2005
4:00 pm
In a celebrated paper, Dyson shows that the spectrum of a random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as non-colliding Brownian motions held together by a drift term. The universal edge, bulk and gap scalings for Hermitian random matrices, applied to the Dyson process, lead to novel stochastic processes,...
• Professor Neshan Wickramasekera
Tue Nov 15, 2005
3:00 pm
I will describe some recent progress on the regularity theory for minimal hypersurfaces. Assuming stability of the hypersurfaces, the results to be presented establish a rather complete local regularity theory that is applicable near points of volume density less than 3. I will also present an existence result. The latter is joint work with Leon...
• Professor Shengli Kong
Tue Nov 8, 2005
4:00 pm
The notion of Extremal K\"ahler metric generalizes both K\"ahler-Einstein metric and K\"ahler metric with constant scalar curvature. Such metric on the blow up of $\mathbb{C}P^n$ in a point was constructed explicitly by Calabi. In this talk, we shall give a different construction of Calabi's metric using Guillemin-Abreu theory on K\"ahler toric...
• Professor Daniel Fox
Tue Oct 25, 2005
4:00 pm
Calibrated submanifolds constitute special classes of minimal submanifolds. Some of the most interesting types of calibrated submanifolds arise inside of manifolds with special holonomy. Integrable systems have been found lurking inside of these special calibrated geometries. Beginning with the work of Haskins and Joyce on special Lagrangian...
• Professor Simon Brendle
Tue Oct 18, 2005
3:00 pm
Let $M$ be a compact manifold of dimension $n \geq 3$. Along the > Yamabe flow, a Riemannian metric on $M$ is deformed according to the > equation $\frac{\partial g}{\partial t} = -(R_g - r_g) \, g$, where $R_g$ > is the scalar curvature associated with the metric $g$ and $r_g$ denotes > the mean value of $R_g$. > > It is known...
• Professor Robert McCann
Tue Oct 18, 2005
2:00 pm