On the existence of holomorphic curves in compact quotients of SL(2,C)

Abstract

In my talk, I will report on recent joint work with I. Biswas, S. Dumitrescu and S. Heller showing the existence of holomorphic maps from a compact Riemann surface of genus g>1 into a quotient of SL(2,C) modulo a cocompact lattice which is generically injective. This gives an affirmative answer to a question raised by Huckleberry and Winkelmann and by Ghys. The proof uses ideas from harmonic maps into the hyperbolic 3-space, WKB analysis, and the grafting of real projective structures.

Speaker

I was born in Wuhan and grew up in the little German town Göttingen, which was home to an extraordinary amount of great Mathematicians (and Nobel prize winners) including all the Mathematicians discussed in the course. I studied economics at the FU Berlin and Mathematics at TU Berlin from 2003-2007 and obtained my PhD from Eberhard Karls University Tübingen in 2012. Thereafter, I stayed in Tübingen as a Postdoc till I got a Juniorprofessorship in 2017 at the Leibniz University in Hannover.

Currently I aim at answering Differential Geometric questions arising in the study of constant mean curvature surfaces as well as (constrained) Willmore surfaces (in 3−dimensional space forms) by combining techniques from Geometric Analysis, Integrable Systems (e.g., Hitchin System) and Algebraic Geometry (e.g.,Higgs bundles and moduli spaces).