February 2018 |

4:00 pm Wednesday, March 21, 2018 Stulken Seminars: Geometry-Analysis: On cyclic Higgs bundlesby Qiongling Li (Caltech) in HBH 227- Given a closed Riemann surface and a Lie group G, the non-abelian Hodge theory gives a correspondence between the space of representations of the surface group into G with the moduli space of G-Higgs bundles. The correspondence is through looking for an equivariant harmonic map to the symmetric space associated to G, to a given representation or a given Higgs bundle. We derive a maximum principle for a type of elliptic systems and apply it to study cyclic Higgs bundles. We show several domination results on the pullback metric of the (possibly branched) minimal immersion associated to cyclic Higgs bundles. Also, we obtain a lower and upper bound of the extrinsic curvature of the image of the minimal immersion. This is joint work with Song Dai.
Submitted by mwolf@rice.edu |