Fecha y lugar: Lunes 24 febrero 2020, 4:45pm, Salón Diego Bricio

Speaker: Travis Wilse, CIMAT

Title: Conformal invariants and the ambient metric construction

Abstract: Invariants of conformal classes of Riemannian metrics, as well as differential operators that depend only on such a class, are tedious to construct directly, and the number of invariants one can construct by hand is small. The ambient metric construction essentially assigns to any conformal class on an n-manifold a Lorentzian metric on an (n + 2)-manifold and so allows us to interpret Riemannian invariants as conformal invariants. We briefly review the conformal invariants known c. 1980, then describe the ambient metric construction and a procedure for construction therefrom invariants and invariant differential operators for the original conformal class. We describe the useful relationship between the ambient and tractor geometries of a conformal structure. With a view toward constructing ambient metrics with interesting properties (for example, [split] G₂ holonomy), the subject of a subsequent talk, we observe that many interesting classes of conformal structures can be characterized in terms of the holonomy of their ambient metrics.