Past Seminars- Analysis

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  • Paata Ivanisvili
    Tue Oct 16, 2018
    3:00 pm
     In 2006 Carbery raised a question about an improvement on the naïve norm inequality  (||f+g||_p)^p ≤ 2^(p-1)((||f||_p)^p + (||g||_p)^p) for two functions in Lp of any measure space. When f=g this is an equality, but when the supports of f and g are disjoint the factor 2^(p-1) is...
  • Yu Yuan
    Tue May 1, 2018
    3:00 pm
    We survey some new and old uniqueness results for Hessian equations such as special Lagrangian equations, Monge-Ampere equations, and symmetric Hessian equations. In particular, a unified approach to quadratic asymptote of solutions over exterior domains--based on an "exterior" Evans-Krylov, corresponding to Allard-Almgren's...
  • 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 $...