Abstract:

I will present joint work with Max Riestenberg on a new existence criterion for harmonic maps to spaces of non-positive curvature, and give some applications. In the first lecture, I will explain our general existence theorem and its proof, and give some context. In the second lecture, I will apply our theorem to certain quasi-isometric embeddings from the hyperbolic plane to symmetric spaces, which will let us generalize Markovic’s resolution of the Schoen conjecture on universal Teichmuller space to universal higher Teichmuller spaces.

Bio:

Peter Smillie is a research group leader at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. He completed his PhD with Professor Yau at Harvard in 2018, and has also worked at IHES, Caltech, and the University of Heidelberg. He works in differential geometry and higher Teichmuller theory, with additional interests in dynamics, representation theory, and geometric group theory.