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Geometry and Topology Seminar

Friday, May 24, 2019
3:00pm to 5:00pm
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Linde Hall 187
Affine actions with Hitchin linear part
Tengren Zhang, Mathematics Department, National University of Singapore,

We prove that if a surface group acts properly on R^d via affine transformations, then its linear part is not the lift of a PSL(d,R)-Hitchin representation. To do this, we proved two theorems that are of independent interest. First, we showed that PSO(n,n)-Hitchin representations, when viewed as representations into PSL(2n,R), are never Anosov with respect to the stabilizer of the n-plane. Following Danciger-Gueritaud-Kassel, we also view affine actions on R^{n,n-1} as a geometric limit of isometric actions on H^{n,n-1}. The second theorem we prove is a criterion for when an affine action on R^{n,n-1} is proper, in terms of the isometric actions on H^{n,n-1} that converge to it. This is joint work with Jeff Danciger, with some overlap with independent work by Sourav Ghosh.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].