## Past Seminars- Analysis

• Ming Xiao
Tue Nov 21, 2017
3:00 pm
We discuss rigidity results of volume-preserving maps between Hermitian symmetric spaces, based on the work of Mok-Ng and my recent joint work with Fang and Huang. Moreover, we make connections with rigidity results in CR geometry.
• Connor Mooney
Tue Sep 26, 2017
3:00 pm
We will discuss examples of singularity formation from smooth data for linear and quasilinear uniformly parabolic systems in the plane.
• Chen-Yun Lin
Tue May 23, 2017
3:00 pm
High-dimensional data can be difficult to analyze. Assume data are distributed on a low-dimensional manifold. The Vector Diffusion Mapping (VDM), introduced by Singer-Wu, is a non-linear dimension reduction technique and is shown robust to noise. It has applications in cryo-electron 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), 445-453), and later developed by Kiselev (Adv. Math. 227 no. 5 (2011), 1806-1826) 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 uniform-in-...
• 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.
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