[WPTADS] Weil–Petersson Teichmüller Space via Anti-de Sitter Geometry
Ente: EC
Scadenza: 2029-08-31
Importo max: 200.400 EUR
Paese: EU
Descrizione
This project aims to build a new connection between the Weil–Petersson Teichmüller (WPT) space and three-dimensional Lorentzian geometry—two important areas of mathematics that have mostly remained separate. A useful setting for exploring this connection is Anti-de Sitter (AdS) geometry, which is a model of a Lorentzian space with constant negative curvature. In the 1990s, Mess made an important step in linking AdS geometry to Teichmüller theory by showing how the geometry of three-dimensional AdS spaces relates to the theory of hyperbolic surfaces. However, many aspects of the WPT space remain largely unexplored within this Lorentzian framework.
The WPT space is an infinite-dimensional Kähler manifold. It arises in several areas of mathematics, including geometric function theory, operator theory, and stochastic processes such as Schramm–Loewner Evolution. Recent work by Bishop (2024) has highlighted new connections between this space and three-dimensional hyperbolic geometry. This project will explore how the WPT space manifests within the context of AdS geometry.
The central objective of the project is to explore the geometric structure of the WPT space through its connection with AdS geometry. In particular, the project aims to relate key analytic features, such as the Kähler potential, to global geometric quantities arising from maximal surfaces in AdS space. More broadly, it will study how natural geometric deformations—such as the earthquake flow—reflect the symplectic and dynamical nature of the WPT space.
This project integrates distinct areas of mathematics in a novel and promising way. It will be supervised by Prof. Jean–Marc Schlenker at the University of Luxembourg, an expert in both AdS geometry and Teichmüller theory. A secondment at ETH Zürich with Prof. Yilin Wang, whose work links Teichmüller theory and probability, will offer a valuable opportunity to broaden my mathematical expertise and develop interdisciplinary skills.
Settori: Horizon Europe Topics
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