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Differential Geometry Seminar Schedule for Fall 2015

Fridays 3:00 - 3:50pm, SH 6635

8/25   3:30pm  Lizhuang Ma,   Shanghai Jiao Tong University  "Techniques and System for Intelligent Processing and Generations for Big
Data of Visual Media"

Abstract:  It is an emerging research area for the applications of intelligent
generation and processing of big data. Big data comes usually from
various sources such as information media, sensors, surveillance,
Internet websites, medical records, scientific research and so on. In
this talk, we focus on the intelligent generation and processing of big
data from visual data, such as digital media, animation, images and
videos from internet.  We try to give an overview of the demand and
background for big data, especially, the visual media. The research goal
for the analyzing and processing of massive media, and desired progress
in the study of different aspects of big data of visual media. Sample
applications for these techniques and systems are given with the recent
progress in the cooperation with the IT giant, Tencent Company, for
examples, the customized compression of massive pictures from internet,
and the face annotation and recognition based on social network.

10/23 Ruobing Zhang, Princeton University,"Quantitative Nilpotent Structure and Regularity of Collapsed Einstein Manifolds"

Abstract: In this talk we discuss the regularity of Einstein manifolds and more generally manifolds with just bounded Ricci curvature, in the collapsed setting. A key tool in the regularity theory of noncollapsed Einstein manifolds is the following: If a bigger geodesic ball on an Einstein manifold $M^n$ is sufficiently Gromov-Hausdorff-close to a ball in $\dR^n$, then in fact the curvature on a smaller ball is uniformly bounded. No such results are known in the collapsed setting, and in fact it is easy to see without more such results are false. It turns out that the failure of such an estimate is related to topology. Our main theorem is that for the above setting in the collapsed context, there is a correspondence between a priori curvature estimates and the local nilpotent rank. There are generalizations of this result to bounded Ricci curvature and even just lower Ricci curvature. This is joint work with Aaron Naber.

11/6 Zhiqin Lu, UCI,  "The essential spectrum of p-forms on complete manifold"

Abstract:  In this talk, I will first give a review of the essential spectrum of the Laplacian on functions over a complete noncompact manifold, and then I will give a preliminary report on the  recent development on locating the essential spectrum of p-forms on complete asymptotically flat manifold. This is joint with Neila Charalambous.

11/13 Meng Zhu, UCR,  " Li-Yau bounds under nearly optimal curvature conditions"

Abstract: We will introduce two new Li-Yau bounds for the heat equation on manifolds under some new curvature conditions. The first one is obtained  for n-dimensional manifolds with fixed Riemannian metric  under the condition that the Ricci curvature being L^p bounded for some p>n/2 or certain Kato type norm of the Ricci curvature tensor being bounded. The second one is proved for manifolds evolving under the Ricci flow with uniformly bounded scalar curvature. As a application, we will also apply the first Li-Yau bound to generalize Colding-Naber's results on parabolic approximations of distance functions to weaker curvature condition setting (most of which were first due to Tian-Z. Zhang ). This is a recent joint work with Qi S. Zhang.

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