From the random geometry of conformally invariant systems to the Kähler geometry of universal Teichmüller space

2023/08/10 by Yilin Wang, Wang, Yilin
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2308.05301

openalex publication_date 2023/08/10 · openalex created_date 2023/08/12 · openalex updated_date 2026/07/28

Abstract

The goal of this expository article is to explain how a fundamental functional on the space of Jordan curves arising from SLE - Loewner energy - is connected to a seemingly far apart subject: the Kähler geometry of universal Teichmüller space. We provide a background on Loewner energy, the universal Liouville action, and the intuition behind the proof of the identity between them.

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