Project description
Exploring connections between hyperbolic surfaces and Lorentzian geometry
The interplay between geometry and analysis could reveal unexpected connections that deepen understanding of mathematical structures. Supported by the Marie Skłodowska-Curie Actions programme, the WPTADS project will explore a new link between the Weil-Petersson Teichmuller space (a geometric structure describing hyperbolic surface deformation) and 3D Lorentzian geometry, which models spacetimes with constant negative curvature such as Anti-de Sitter (AdS) spaces. WPTADS will study how the infinite-dimensional Weil-Petersson space relates to maximal surfaces (objects that minimise area) in AdS geometry. It will also examine how natural deformations, including earthquake flows, reveal the symplectic and dynamical properties of the space. By bridging these areas, WPTADS aims to provide new clues to hyperbolic and Lorentzian geometry.
Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences earth and related environmental sciences geology seismology
- natural sciences mathematics pure mathematics geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2025-PF
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
4365 ESCH-SUR-ALZETTE
Luxembourg
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.