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Time and venue: Unless otherwise stated, seminars are on Wednesdays at 3pm. These take place on Zoom or in person, usually in Roger Stevens LT 11. When on Zoom we will still meet (when possible) to view the Zoom seminar. Further Geometry and Analysis group activities and information may be found here. Programme Semester 2: 29 January - 15:00 - Roger Stevens LT11 - in person Luca Seemungal (University of Leeds) The Index of Constant Mean Curvature Surfaces in Three-Manifolds Abstract. Constant mean curvature (CMC) surfaces are special geometric variational objects, closely related to minimal surfaces. The key properties of a CMC surface are its area, mean curvature, genus, and index. The index of a CMC surface measures its stability: the index counts how many ways one can perturb the surface to decrease the area while keeping the enclosed volume constant. In this talk we discuss relationships between these key properties. In particular we present recent joint work with Ben Sharp, where we bound the index of CMC surfaces linearly from above by genus and the correct scale-invariant quantity involving mean curvature and area. 5 February - 15:00 - Roger Stevens LT11 - in person Enric Solé-Farré (University College London and Imperial College London) The Hitchin and Einstein indices of cohomogeneity one nearly Kähler manifolds Abstract. Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001. The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption. 12 February - 15:00 - Roger Stevens LT11 - in person JeongHyeong Park (Sungkyunkwan University) Curvature identities and their applications Abstract. Is there a curvature identity that holds on any Riemannian manifold? Through the Chern-Gauss-Bonnet theorem, we can derive curvature identities that apply to 4-dimensional or 6-dimensional Riemannian manifolds. As an application of curvature identities, we prove Lichnerowicz’s conjecture in 4 dimensions under a slightly more general setting. Furthermore, we explore weakly Einstein manifolds, which arise as a generalization of 4-dimensional Einstein manifolds through the application of curvature identities. We also investigate the existence and non-existence of weakly Einstein metrics on certain Lie groups in recent studies, and propose a conjecture based on these results. (This is joint work with Y. Euh, S. Kim and Nikolayevsky.) 19 Febraury - 15:00 - Roger Stevens LT11 - in person Martin Palmer-Anghel (University of Leeds) 26 February - 15:00 - Roger Stevens LT11 - in person Veronique Fischer (University of Bath) 5 March - 15:00 - Roger Stevens LT11 - in person Valentino Magnani (University of Pisa) 12 March - 15:00 - Roger Stevens LT11 - in person/on zoom TBC 19 March - 15:00 - Roger Stevens LT11 - in person Sam Collingbourne (University of Edinburgh) 26 March - Yorkshire Durham Geometry Day in York 30 April - 15:00 - Roger Stevens LT11 - in person/on zoom TBC 7 May - 15:00 - Roger Stevens LT11 - in person/on zoom TBC Geometry Seminar 2023-2024: Semester 1/Semester 2 Geometry Seminar 2022-2023: Semester 1/Semester 2 Previous Leeds Geometry Seminars |