Past Seminars- Analysis

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  • 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.
  • 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 well-known properties of the Fourier transform....
  • Jeffrey Case
    Tue Feb 7, 2017
    3:00 pm
    The P-prime operator is a CR invariant operator on CR pluriharmonic functions and is closely related to a sharp Moser--Trudinger-type 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-...