Ben Sibley, Simons Center, Stony Brook University
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