
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 genustwo curves particularly, asymptotic formulas with precise coefficients...

Jian Song
Tue Apr 3, 2018
3:00 pm
We discuss general compactness results for KahlerEinstein manifolds of negative scalar curvature and geometric KahlerEinstein metrics on smoothable semilog 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 realanalytic 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 XuJia Wang and QiRui 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 HardyAdams inequalities on hyperbolic balls and HardySobolevMazya inequalities on upper half spaces or hyperbolic balls. Using the Fourier analysis on hyperbolic spaces, we will be able to establish sharper...