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Differential Geometry Seminar
Differential Geometry Seminar
New Spin(7) Metrics with Generic Aloff–Wallach Spaces as Principal Orbits
New Spin(7) Metrics with Generic Aloff–Wallach Spaces as Principal Orbits
Organizers
Kenji Fukaya
, Lynn Heller
, Sebastian Heller
, Kotaro Kawai
,
Enric Sole Farre
Speaker
Hanci Chi
Time
Tuesday, March 10, 2026 2:30 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
In this talk, we present new families of complete non-compact Spin(7) metrics with distinct topological types. These metrics arise as integral curves of the cohomogeneity one Ricci-flat equations, where the principal orbit is a generic Aloff–Wallach space. The problem can be formulated as a dynamical system on an algebraic surface. By constructing an invariant subset in the compactified phase space, we establish the existence of 1-parameter families of ALC Spin(7) metrics that converge, in a suitable limit, to AC metrics. In particular, this provides topologically distinct resolutions of a single Spin(7) cone, a phenomenon of both mathematical and physical interest.