Past Events

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal...

We present an analog of the total variation image reconstruction approach by Rudin, Osher, Fatemi (1992) for images defined on smooth surfaces, together with a proper analytical framework. The problem is defined in terms of quantities intrinsic to...

In this talk, we consider the well-posedness, ill-posedness and the regularity of stationary solutions to the hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary, and make a classification on these...

A spectral method for the solution of integral and differential equations is generally understood to be an expansion of the solution in a Fourier series. Chebyshev polynomials are often the preferred basis set for many problems. In kinetic theory...

Transformation Optics (aka transformation media) offers an unprecedented method of manipulating a variety of waves through architecting the propagation medium. The necessary condition for a wave to be controllable by this method is that its governing...

I will discuss finite group actions on integral or rational homology 3-spheres. The main examples for this talk are the Brieskorn integral homology 3-spheres M(p,q,r) arising from isolated singularities, which bound smooth 4-manifolds with definite...

Penalized regression methods permit data analysts to fit models with more adjustable parameters than data points by imposing strong prior assumptions on the relationships between variables. As a result classical tools of uncertainty assessment no...

L^p inequalities for certain Littlewood-Paley functionals arising from Lévy processes will be discussed. These are motivated by applications to the L^p boundedness of Fourier multiples which give L^p regularity of solutions to some non-local...

We will discuss about the regularity of the Gauss curvature flow: the optimal C^{1,\frac{1}{n-1}} regularity of degenerate solutions with flat sides and the interior C^{\infty} regularity of strictly convex solutions.