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Title: Geodesic Rays in the Donaldson-Uhlenbeck-Yau Theorem.

Abstract:The theorem of Donaldson-Uhlenbeck-Yau says that a holomorphic vector bundle E over a compact Kahler manifold admits a Hermite-Einstein (HE) metric iff E is stable. Historically, this was the first example of a general program linking solvability of certain geometric PDE (the HE metric) with an (algebraic) stability condition, and is something of a spiritual predecessor to the Yau-Tian-Donaldson conjecture. Work on this subsequent conjecture has revealed an important link with a third object, namely, geodesic rays of ``weak" metrics. In joint work with Jonsson, Shivaprasad, we return to the DUY theorem and, by focusing on the analogous geodesic rays in this setup, find a new proof of this celebrated work.

UQAM - PK-5115, 201 ave President-Kennedy et Zoom