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Differential Geometry: "Positive curvature in dimension 7"

Owen Dearricott, UC Riverside

Friday, November 3, 2017
  11:10 a.m.–Noon

Location: Surge Building 268
  Parking Information

Category: Seminar


In their 2008 paper Grove, Wilking and Ziller proposed two infinite families, P_k and Q_k where k>1,  of simply connected manifolds in dimension 7 that may carry Riemannian metrics with positive curvature whose isometry groups' principal orbits are hypersurfaces.  The two families occur as double covers of certain 3-Sasakian manifolds given by the total spaces of the Konishi-bundles of certain self-dual Einstein metrics on orbifold 4-spheres described by Hitchin in the early 90s.  To date only one of these proposed candidates, P_2, is known to actually carry a metric with positive sectional curvature and the techniques employed in that case do not directly generalise to the series of candidates.

In this talk we discuss a promising new technique that should work to put positive curvature on the two series as it applies to the candidates Q_2 and P_3.

Additional Information: Math Seminars

Open to: General Public
Admission: Free
Sponsor: Mathematics

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