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Removability of Planar Sets Pt II

[HYBRID WORKSHOP] Introductory Workshop: The Analysis and Geometry of Random Spaces January 24, 2022 - January 28, 2022

January 28, 2022 (09:50 AM PST - 10:40 AM PST)
Speaker(s): Malik Younsi (University of Hawaii at Manoa)
Location: SLMath: Online/Virtual
Tags/Keywords
  • Conformal maps

  • quasiconformal mappings

  • removability

  • conformal welding

  • Koebe's conjecture

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

Removability Of Planar Sets Pt. II

Abstract

Ever since the seminal work of Ahlfors and Beurling in the 1950's, the study of removable planar sets with respect to various classes of holomorphic functions has proven over the years to be of fundamental importance for a wide variety of problems in complex analysis and related areas. Questions revolving around necessary and sufficient geometric conditions for removability have held a prominent role in the development of valuable techniques and applications.

In recent years, attention has been drawn to the more modern notion of (quasi)conformal removability, in view of applications to an ever-growing variety of central problems in complex analysis, probability and dynamics. In this talk, I will discuss various results related to conformal removability, focusing on applications to conformal welding and to Koebe's uniformization conjecture.

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Removability Of Planar Sets Pt. II

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