Noncompact Ricci flat Kahler and Hyperkahler metrics

Eugenie Hunsicker

3.00pm-5.00 pm February 15

380-383N (Math lounge), Stanford
ABSTRACT: I will present three classes of noncompact Ricci-flat Kahler metrics, two constructed by Tian and Yau as solutions to the noncompact Calabi conjecture, and the QALE metrics of Dominic Joyce (with special case ALE metrics). The metrics of Tian and Yau come with a natural compactification. The asymptotics of these metrics can be described in terms of this compactification, as can some results and conjectures about L^2 harmonic forms on these manifolds. The ALE spaces of Joyce also have a natural compactification, and this permits a description of $L^2$ harmonic forms on these spaces, as well. I will discuss possible generalizations of this compactification to the QALE case.
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