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Loewner Energy, SLE and Weil-Petersson Quasicircles

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

January 24, 2022 (10:20 AM PST - 11:10 AM PST)
Speaker(s): Wang Yilin (Massachusetts Institute of Technology)
Location: MSRI: Simons Auditorium, Online/Virtual
  • Loewner energy

  • SLE

  • Weil-Petersson quasicircle

  • large deviations

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Secondary Mathematics Subject Classification

Loewner Energy, SLE And Weil-Petersson Quasicircles


This is an introductory lecture on the Loewner energy and its links to Schramm-Loewner evolutions and Weil-Petersson quasicircles, a class of Jordan curves arising from the Kahler geometry on the universal Teichmuller space. This class of curves is also of interest in geometric function theory and has many drastically different but equivalent definitions. These links show that the Loewner energy sits at the crossroad of random conformal geometry and analysis. After explaining the basic definitions and the main connections, I will focus on the related open questions.

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Loewner Energy, SLE And Weil-Petersson Quasicircles

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