Topology and geometry of higher Teichmüller spaces
The project investigates the geometry and topology of higher rank Teichmüller spaces, focusing especially on the Hitchin components and maximal representations. It combines techniques from differential geometry, geometric analysis, affine differential geometry, and Higgs bundle theory.
The central objective is to understand geometric structures associated to surface group representations into higher rank Lie groups. This includes: compactifications of Hitchin components, global geometry of deformation spaces and new geometric transitions between different higher rank Teichmüller spaces. The project tackles major open problems, including the boundary of Hitchin components and the geometry of para-hyperKähler and pseudo-Kähler structures.
Open Positions
The project will fund a dynamic research group, including five postdoctoral researchers and two PhD students. The positions are staggered throughout the project according to the official plan.
PhD Positions
- Number of positions: 2
- Start date: October 2026
- Duration: 3 years
- Description: The PhD students will work full-time on the project, receiving extensive training and collaborating closely with other members of the group.
Postdoctoral Positions
The project funds 5 postdocs in total, employed at different stages of the 5-year period:
- Two 3-year postdoc positions : starting as early as September 2026.
- Three 2-year postdoc positions : starting in the spring of 2029.
- Research areas: geometric analysis, Higgs bundles, (affine) differential geometry, Anosov representations.
For all postdoc positions, candidates should have a strong background in at least one of: geometric analysis, differential geometry, Teichmüller theory, Higgs bundles, or related areas. The positions are full-time and research-only, with no teaching obligations.
How to Apply
Applications will be announced through the University of Pisa portal and relevant mathematics job boards. Interested candidates may contact the PI:
Email: andrea_tamburelli@libero.it