## Speaker:

Greg Lawler

## Speaker Link:

## Institution:

University of Chicago

## Time:

Friday, February 24, 2017 - 2:00am to 3:00am

## Host:

## Location:

NS2 1201

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).