Geometric Analysis Seminar: Hadrian Quan (UC Santa Cruz)

Title: The Ambient construction and its descendents on KE, CR, QK, and QC spaces

Abstract: In conformal geometry, the Ambient construction of Fefferman-Graham relates conformal invariants of a closed manifold M to (pseudo-)Riemannian invariants of a certain non-compact space X which realizes M as its ``conformal boundary." This formalism has a long history and many connections throughout the geometric analysis of (asymptotically) hyperbolic manifolds, and mathematical physics. Almost as long-established is a similar correspondence where real hyperbolic models are replaced with their complex analogues, and Lorentzian K\"ahler-Einstein spaces are constructed to bound conformal *CR* manifolds. In this talk I will report on on-going work to study a quaternionic analogue of this construction, with a focus on how this approach can be used to create conformally invariant differential operators in the corresponding boundary geometry.