Tuesday, January 24, 2023
01/24/2023 - 4:15pm
Abstract: Labourie proved that every Hitchin representation into PSL(n,R) gives rise to an equivariant minimal surface in the corresponding symmetric space. He conjectured that uniqueness holds as well (this was known for n=2,3) and explained that if true, then the Hitchin component admits a mapping class group equivariant parametrization as a holomorphic vector bundle over Teichmüller space. After giving the relevant background, we will explain that Labourie’s conjecture fails for n at least 4, and point to some future questions.