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The Analyst's Traveling Salesman Theorem for large dimensional objects

Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017

May 18, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Jonas Azzam (University of Edinburgh)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • geometric incidence problem

  • complex analysis

  • harmonic measure

  • harmonic analysis

  • Traveling Salesman Theorem

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Azzam

Abstract

The classical Analyst's Traveling Salesman Theorem of Peter Jones gives a condition for when a subset of Euclidean space can be contained in a curve of finite length (or in other words, when a "traveling salesman" can visit potentially infinitely many cities in space in a finite time). The length of this curve is given by a square sum of quantities called beta-numbers that measure how non-flat the set is at each scale and location. Conversely, given such a curve, the square sum of its beta-numbers is controlled by the total length of the curve, giving us quantitative information about how non-flat the curve is. This result and its subsequent variants have had applications to various subjects like harmonic analysis, complex analysis, and harmonic measure. In this talk, we will introduce a version of this theorem that holds for higher dimensional surfaces. This is joint work with Raanan Schul.

Supplements
28691?type=thumb Azzam Notes 1.54 MB application/pdf Download
Video/Audio Files

Azzam

H.264 Video 11-Azzam.mp4 247 MB video/mp4 rtsp://videos.msri.org/data/000/028/475/original/11-Azzam.mp4 Download
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