
ChenYun Lin
Tue May 23, 2017
3:00 pm
Highdimensional data can be difficult to analyze. Assume data are distributed on a lowdimensional manifold. The Vector Diffusion Mapping (VDM), introduced by SingerWu, is a nonlinear dimension reduction technique and is shown robust to noise. It has applications in cryoelectron microscopy and image denoising and has...

Sean Curry
Tue Apr 25, 2017
3:00 pm
The problem of understanding CR geometries embedded as submanifolds in
higher dimensional CR manifolds arises in higher dimensional complex
analysis, including the study of singularities of analytic
varieties. It has also been studied intensively in connection with
rigidity questions. Despite considerable earlier work the local theory
has not been...

Liutang Xue
Tue Apr 11, 2017
3:00 pm
The method of nonlocal maximum principle was initiated by Kiselev et al (Inve. Math. 167 (2007), 445453), and later developed by Kiselev (Adv. Math. 227 no. 5 (2011), 18061826) and other works. The general idea is to show that the evolution of considered equation preserves a suitable modulus of continuity, so that one gets the uniformin...

Changfeng Gui
Tue Mar 14, 2017
3:00 pm
In this talk, I will introduce a new geometric inequality: the Sphere Covering Inequality. The inequality states that the total area of two {\it distinct} surfaces with Gaussian curvature less than 1, which are also conformal to the Euclidean unit disk with the same...

Xiaodong Wang
Tue Mar 7, 2017
4:00 pm
Given a compact Riemannian manifold with nonnegative Ricci curvature and convex boundary it is interesting to estimate its size in terms of the volume, the area of its boundary etc. I will discuss some open problems and present some partial results.
This is a joint seminar with geometry.

Russell Brown
Tue Mar 7, 2017
3:00 pm
We consider the scattering map introduced by Beals and Coifman and Fokas and Ablowitz that may be used to transform one of the Davey Stewartson equations to a linear evolution. We give mapping properties of the scattering transform on weighted L^2 Sobolev spaces that mimic wellknown properties of the Fourier transform....

Jeffrey Case
Tue Feb 7, 2017
3:00 pm
The Pprime operator is a CR invariant operator on CR pluriharmonic functions and is closely related to a sharp MoserTrudingertype inequality in CR manifolds. I will describe some analytic and geometric properties of this operator, and in particular use it to solve a nonlinear PDE of critical order which is the CR analogue of the Q...