Speaker: Ruobing Zhang, Princeton University

Title: Collapsing geometry and moduli space of Einstein metrics in dimension four
Abstract: This talk focuses on the recent resolution of the following conjectures in the study of Ricci-flat four manifolds.

(1) Any volume collapsed limit of unit-diameter Einstein metrics on the K3 manifold is isometric to one of the following: the quotient of a flat 3D torus by an involution, a singular special Kaehler metric on the topological 2-sphere, or the unit interval.

(2) Any complete non-compact hyperkaehler 4-manifold with quadratically integrable curvature, namely gravitational instanton, must have one of the following asymptotic model geometries: ALE, ALF, ALG, ALH, ALG* and ALH*.
We will also discuss some applications and further directions.

Engineering and Computer Science West (ECSW), ECSW 1.315
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics
Stephen E. McKeown

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  • Leah Sullivan

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