Past Seminars- Analysis

Printer-friendly version
  • Slawomir Dinew
    Thu Aug 11, 2016
    4:00 pm
     We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Ampere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we prove that the minimum set cannot contain analytic subvarieties of large dimension. In the planar case...
  • Xinan Ma
    Tue May 24, 2016
    3:00 pm
    For the Dirichlet problem on the k Hessian equation, Caffarelli-Nirenberg-Spruck (1986) obtained the existence of the admissible classical solution when the smooth domain is strictly k-1 convex in R^n. In this talk, we prove the existence of a classical admissible solution to a class of Neumann boundary value problems for k Hessian equations...
  • Yu Yuan
    Tue May 10, 2016
    3:00 pm
    We survey some new and old, positive and negative results on a priori estimates, regularity, and rigidity for special Lagrangian equations with or without certain convexity. The "gradient" graphs of solutions are minimal or maximal Lagrangian submanifolds, respectively in Euclidean or pseudo-Euclidean spaces. In the latter pseudo-...
  • Siqi Fu
    Thu Apr 21, 2016
    4:00 pm
    In this expository talk we will discuss aspects of spectral theory of the complex Laplacian, revolving around the notion of positivity.  We will discuss geometric/potential theoretic characterizations for positivity of the complex Neumann Laplacian and explain some applications of the theory in complex geometry.
  • Yuan Yuan
    Thu Mar 31, 2016
    3:00 pm
    We will discuss the common submanifolds of two Hermitian symmetric spaces. In particular, we proved that the Euclidean space and a bounded symmetric domain cannot share a common submanifold. This is based on the joint work with Professor X. Huang.
  • Robin Graham
    Tue Feb 16, 2016
    3:00 pm
    Geodesics in hyperbolic space, or more generally in an asymptotically hyperbolic manifold, have infinite length as they approach the boundary at infinity.  Nonetheless, it is possible to associate a finite renormalized length to such a geodesic.  This talk will describe how one can recover the infinite order boundary jet of an...
  • Josh Strong
    Tue Feb 9, 2016
    3:00 pm
    One way to classify bounded domains of several complex variables is to determine the boundary behavior.  It is a conjecture of Greene and Krantz that if an automorphism orbit accumulates at the boundary of a smooth domain, then that point is of finite type in the sense of D'Angelo.  We will discuss some supporting results and a...