Recent Developments in Special and Exceptional Holonomy Metrics. Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics Third Annual Meeting. Simons Foundation. September 13, 2019

International Meeting or Conference

In this talk, Haskins will give an overview of some of the main recent developments in the construction of metrics with special and exceptional holonomy, concentrating on the progress made by members of the collaboration on resolving some long-standing open questions. He will indicate some of the symbiotic relationships that have developed between the two better understood cases of hyperKaehler 4-manifolds and Calabi-Yau 3-folds, and the more challenging case of 7-manifolds with holonomy G2. One important unifying theme has been the more systematic study of special or exceptional holonomy metrics in either highly collapsed regimes or close to a suitable adiabatic limit: codimension one (circle) collapse of G2 holonomy metrics underpins the physical limit where M theory is modeled by Type IIA string theory; collapsed Calabi-Yau metrics with fibers close to flat tori appear in connection with degenerations of complex structure; K3 fibrations of Calabi-Yau 3-folds or coassociative K3 fibrations of G2 manifolds with small fiber size also both appear naturally. The latter adiabatic limit will be discussed in more detail in Simon Donaldson’s talk.

Service Performed By

Date

  • September 13, 2019

Service or Event Name

  • Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics Third Annual Meeting

Host Organization

  • Simons Foundation

Location or Venue

  • Manhattan, New York