Department Colloquium

Abstract: When is a map between complete noncompact Riemannian manifolds at bounded distance from a harmonic map? Does a quasi-symmetric self-map of the circle always extend to a harmonic self-map of the hyperbolic plane? The answer to the second question is yes, by celebrated work of Markovic. In this talk, I will present recent work with Max Riestenberg giving a general sufficient criterion for the first question, which also recovers the answer to the second. The proof uses some elementary geometric ideas, which I will explain.

But our real motivation is that our criterion also lets us answer an analog of the second question for harmonic maps to higher rank symmetric spaces. I’ll explain why we care so much about this question, which connects universal Teichmuller space, higher Teichmuller theory, and non-Abelian Hodge theory.