# Limiting Properties of the Yang-Mills flow on Kahler Manifolds

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Benjamin Sibley, University of Maryland
Fine Hall 314

In this talk, I will give a result about the limit of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary Kähler manifold (X;ω). In particular, this theorem says that the flow is determined at infinity by the holomorphic structure of E. Namely, if we fix an integrable unitary reference connection A0 defining the holomorphic structure, then the Yang-Mills flow with initial condition A0, converges (away from an appropriately defined singular set) in the sense of the Uhlenbeck compactness theorem to a holomorphic vector bundle E, which is isomorphic to the associated graded object of the Harder-Narasimhan-Seshadri ltration of (E;A0). Moreover, E extends as a reexive sheaf over the singular set as the double dual of the associated graded object. This is an extension of previous work in the cases of 1 and 2 complex dimensions and proves the general case of a conjecture of Bando and Siu.