Minimal Surfaces in Symmetric Spaces and Labourie's Conjecture

Explore a mathematical lecture that delves into the counterexamples to Labourie's Conjecture through the study of minimal surfaces in symmetric spaces. Learn how Hitchin representations from pi_1(S) to PSL(n,R) serve as natural generalizations of Fuchsian representations to PSL(2,R), and understand their relationship to hyperbolic metrics on closed surfaces of genus 2 or higher. Discover the process of producing large area minimal surfaces that contradict Labourie's uniqueness conjecture for all n≥4, while gaining insights into harmonic maps and minimal immersions to symmetric spaces. Examine the connection between these findings and the theory of harmonic maps to buildings, presented through collaborative research with Peter Smillie.