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Abstract: Following Lars Sektnan's talk on optimal symplectic connections and stability of fibrations [on 29 January, see http://indico.ictp.it/event/9539/], I will present new work in this area. The main result is that a fibration admitting an optimal symplectic connection is polystable with respect to a certain large class of fibration degenerations, which builds on a previous result obtained by Dervan and Sektnan. To prove this, we analyse geodesics in the space of all fibrewise cscK (constant scalar curvature Kähler) metrics, and show that a natural log-norm functional on this space is convex along geodesics. Along the way, we use the tools developed to give a new and illuminating proof that optimal symplectic connections are unique up to automorphisms within a fixe relatively Kähler class (another result due to Dervan and Sektnan).
This work is for my PhD thesis, supervised by Ruadhaí Dervan and Frances Kirwan.
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