ICTP-SISSA Math Seminar on Kähler Geometry (Zoom Meeting) - Friday 5 February at 14:00 (Michael Hallam)

[ICTP Math Section]

ICTP-SISSA Math Seminar on Kähler Geometry


Friday 5 February, at 14:00, Central European Time



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Speaker: Michael Hallam (OxfordUniversity)

Title: Stability of Fibrations through Geodesic Analysis

Abstract: Following Lars Sektnan's talk on optimal symplectic 
connections and stability of fibrations [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./