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SUMMARY:Raanan Schul (Stony Brook University)
DTSTART:20240110T123000Z
DTEND:20240110T143000Z
DTSTAMP:20260423T023942Z
UID:NCTS-GMT/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/21/
 ">Uniformly rectifiable metric spaces</a>\nby Raanan Schul (Stony Brook Un
 iversity) as part of NCTS international Geometric Measure Theory seminar\n
 \n\nAbstract\nIn their 1991 and 1993 foundational monographs\, David and S
 emmes characterized uniform rectifiability for subsets of Euclidean space 
 in a multitude of geometric and analytic ways. The fundamental geometric c
 onditions can be naturally stated in any metric space and it has long been
  a question of how these concepts are related in this general setting. In 
 joint work with D. Bate and M. Hyde\, we prove their equivalence. Namely\,
  we show the equivalence of Big Pieces of Lipschitz Images\, Bi-lateral We
 ak Geometric Lemma and Corona Decomposition in any Ahlfors regular metric 
 space. Loosely speaking\, this gives a quantitative equivalence between ha
 ving Lipschitz charts and approximations by nice spaces. After giving some
  background\, we will explain the main theorems and outline some key steps
  in the proof (which will include a discussion of Reifenberg parameterizat
 ions). We will also mention some open questions.\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/21/
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