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math.DG2023★ 1 cited
Stability conditions and canonical metrics
John Benjamin McCarthy
In this thesis we study the principle that extremal objects in differential geometry correspond to stable objects in algebraic geometry. In our introduction we survey the most famo…
math.DG2022
Canonical metrics on holomorphic fibre bundles
John Benjamin McCarthy
In this article we completely describe the existence of canonical metrics, known as optimal symplectic connections, on isotrivial Kähler fibrations. In this setting an optimal symp…
math.DG2020★ 1 cited
-critical connections and Bridgeland stability conditions
Ruadhaí Dervan, John Benjamin McCarthy, Lars Martin Sektnan
We associate geometric partial differential equations on holomorphic vector bundles to Bridgeland stability conditions. We call solutions to these equations -critical connection…