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Conformal Geometry Program Lecture Series: Greg Lawler, University of Chicago

Greg Lawler, University of Chicago

Title: Minkowski Content and the Schramm-Loewner Evolution
Speaker: Greg Lawler, University of Chicago
Date: Wednesday, April 3, 2013
Time: 4:00pm – 5:30pm
Place: Seminar Room 313, Simons Center

 

 

 

 

Abstract: The d-dimensional Minkowski content of a bounded set in the complex plane is defined to be the the limit as r goes to zero of r^{d-2} times the area of points within distance r of the set. We show that the Minkowski content of a Schramm-Loewner evolution curve with kappa < 8 exists and coincides with the natural parametrization of SLE curves as defined previously. We will sketch the tools of the proof and then we will make the case for why this is the “correct” way to parametrize the curves. This is joint work with Mohammad Rezaei.