Positivity and Higher Teichmüller Spaces

Explore the fascinating world of Teichmüller spaces and positivity in Lie groups through this insightful lecture by Anna Wienhard from the Max Planck Institute for Mathematics in the Sciences. Delve into the history of Hitchin's introduction of Teichmüller components in varieties of representations of surface groups into split real Lie groups of higher rank. Discover how these components are part of a larger class of examples related to positivity in Lie groups. Learn about the relevant notion of positivity, examine positive representations, and understand why they form connected components. Conclude by discussing open questions and conjectures in this field, providing a comprehensive overview of current research in higher Teichmüller spaces.