Geometric Analysis and Topology Seminar

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Gravitational instantons and harmonic maps

Speaker: Mingyang Li, Stony Brook University

Location: Warren Weaver Hall 512

Date: Friday, November 21, 2025, 11 a.m.

Synopsis:

It is known from general relativity that axisymmetric stationary black holes can be reduced to axisymmetric harmonic maps into the hyperbolic plane H^2, while in the Riemannian setting, 4d Ricci-flat metrics with torus symmetry can also be locally reduced to such harmonic maps satisfying a tameness condition. We study such harmonic maps. Applications include a construction of infinitely many new complete, asymptotically flat, Ricci-flat 4-manifolds with arbitrarily large b_2. Joint work with Song Sun.