Past Seminars- Analysis

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  • Xin Dong
    Tue Apr 17, 2018
    3:00 pm
    We study variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a holomorphic family of hyperelliptic nodal or cuspidal curves and their Jacobians, we announce our results on the Bergman kernel asymptotics near various singularities. For genus-two curves particularly, asymptotic formulas with precise coefficients...
  • Jian Song
    Tue Apr 3, 2018
    3:00 pm
    We discuss general compactness results for Kahler-Einstein manifolds of negative scalar curvature and geometric Kahler-Einstein metrics on smoothable semi-log canonical models.    Joint with Differential Geometry Seminar.
  • Bernhard Lamel
    Tue Mar 13, 2018
    4:00 pm
    It is a striking phenomenon of formal maps between real-analytic hypersurfaces that in many circumstances they actually converge. In recent work with Nordine Mir, we were able to characterise (in a suitable sense) divergent maps, leading to many new convergence results. We will discuss these recent results. 
  • Bigyuan Liu
    Tue Feb 27, 2018
    3:00 pm
    In this talk, we discuss the Diederich–Fornæss index in several complex variables. A domain Ω ⊂ Cn is said to be pseudoconvex if −log(−δ(z)) is plurisubharmonic in Ω, where δ is a signed distance function of Ω. The Diederich–Fornæss index has been introduced since 1977 as an...
  • Weimin Sheng
    Tue Jan 30, 2018
    3:00 pm
    In this talk, I will introduce our recent work on Gauss curvature flow with Xu-Jia Wang and Qi-Rui Li. In this work we study a contracting flow of closed, convex hypersurfaces in the Euclidean space $\R^{n+1}$ with the speed $f r^{\alpha} K$, where $K$ is the Gauss curvature, $r$ is the distance from the hypersurface to the origin, and $...
  • Andrew Seth Raich
    Tue Jan 23, 2018
    3:00 pm
    In this talk, I will discuss the strengths and shortcomings of the Fourier transform as a tool to investigate the global analysis of PDEs. As part of this discussion, I will give various applications to problems in several complex variables and introduce a FBI transform as a more broadly applicable tool.  
  • 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...