Title: 50 years of special holonomy.
Abstract: 50 years ago S.T. Yau proved Calabi’s conjecture and thereby established the existence of Riemannian metrics with holonomy group the special unitary group, SU(n) on any compact Kahler manifold with vanishing first Chern class. Such (Kahler Ricci-flat) metrics are usually called Calabi—Yau metrics in their honor. Other Ricci-flat holonomy groups in the Berger classification proved much more elusive and only in 1996 did Joyce first prove the existence of compact 7-manifolds with holonomy group the exceptional simple Lie group G2. Even today G2 holonomy metrics remain much less well-understood than Calabi—Yau metrics.
In this talk we will describe some of the history of the subject and then focus on recent developments regarding the construction (and classification) of complete noncompact manifolds with special or exceptional holonomy, especially in the Calabi—Yau and G_2 settings. We will explain some ways in which recent results about Calabi—Yau metrics have implications for the construction of new G2 holonomy metrics.
Eric Zaslow
(847) 467-6447
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