Abstract: Using results from the theory of harmonic maps, Kotschick proved that a closed hyperbolic four-manifold cannot admit a complex structure. We give a new proof which instead relies on properties of Einstein metrics in dimension four. The benefit of this new approach is that it generalizes to prove that another class of aspherical four-manifolds (graph manifolds with positive Euler characteristic) also fail to admit complex structures. This is joint work with Luca Di Cerbo.

Biography: Michael recently joined the University of Adelaide as a lecturer in the School of Computer and Mathematical Sciences. He obtained his PhD from Stony Brook University in 2019 under the supervision of Claude LeBrun, and completed postdocs at Université du Québec à Montréal and the University of Waterloo.

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