
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...

Ming Xiao
Tue Nov 21, 2017
3:00 pm
We discuss rigidity results of volumepreserving maps between Hermitian symmetric spaces, based on the work of MokNg 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.

ChenYun Lin
Tue May 23, 2017
3:00 pm
Highdimensional data can be difficult to analyze. Assume data are distributed on a lowdimensional manifold. The Vector Diffusion Mapping (VDM), introduced by SingerWu, is a nonlinear dimension reduction technique and is shown robust to noise. It has applications in cryoelectron 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), 445453), and later developed by Kiselev (Adv. Math. 227 no. 5 (2011), 18061826) 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 uniformin...