Ben Sibley, Simons Center, Stony Brook University
"Limits and bubbling sets for the Yang-Mills flow on Kaehler manifolds"
The Yang-Mills flow first appeared in the early 1980s in seminal work of Atiyah and Bott, who conjectured that on a Riemann surface it could be used to define a Morse theory for a certain functional on the space of holomorphic vector bundles, recovering their stratification by Harder-Narasimhan type. This was eventually shown to be the case by Daskalapoulos. Meanwhile, Donaldson had shown the long-time existence for the flow on a Kaehler manifold of any dimension, and the convergence when one starts the flow at a stable holomorphic structure. This left open the question of convergence in higher dimensions in the unstable case. I will discuss a complete (in some sense) solution to this problem, resolving a conjecture of Bando and Siu. This is partly joint work with Richard Wentworth.
MC 5413