Past Seminars- Analysis

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  • Guozhen Lu
    Tue Jan 9, 2018
    3:00 pm
    We will use the techniques of harmonic analysis to establish optimal geometric inequalities. These include the sharp Hardy-Adams inequalities on hyperbolic balls and Hardy-Sobolev-Mazya inequalities on upper half spaces or hyperbolic balls. Using the Fourier analysis on hyperbolic spaces, we will be able to establish sharper...
  • 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...