We propose in this work a fast numerical algorithm for solving the equation of
radiative transfer (ERT) in isotropic media. The algorithm has two steps. In the first
step, we derive an integral equation for the angularly averaged ERT solution by taking
advantage of the isotropy of the scattering kernel, and solve the integral equation
with a fast multipole method (FMM). In the second step, we solve a scattering-free
transport equation to recover the original ERT solution. Numerical simulations are
presented to demonstrate the performance of the algorithm for both homogeneous and
inhomogeneous media.

Abstract: We will consider recent numerous achievements in the area of understanding
the harmonic measure of general domains in\R^n.
These results become possible because of the recent breakthroughs in non-homogeneous
harmonic analysis.

I will present the limiting absorption principle for free Laplacian in the talk, which is based on a article in Terence Tao's  blog.

For a smooth curve, the natural paraemtrization

is parametrization by arc length.  What is the analogue

for a random curve of fractal dimension d?  Typically,

such curves have Hausdorff dmeasure 0.  It turns out

that a different quantity, Minkowski content, is the

right thing.   

I will discuss results of this type for the Schramm-Loewner

evolution --- both how to prove the content is well-defined

(work with M. Rezaei) and how it relates to the scaling

limit of the loop-erased random walk (work with F. Viklund

and C. Benes).