Dept Math & Stat UiT, Forskningsparken B459
  28 Sep 2023 Thu

10:30-11:30

Sam Blitz (Masaryk University Brno)

A New Method of Generating Conformal Submanifold Invariants

The geometry of scale, also known as conformal geometry, is concerned with the study of conformal manifolds - smooth manifolds equipped with an equivalence class of metrics, where equivalence is up to multiplication by a positive function. Of particular interest is the problem of classifying invariants of such a structure. Over the last 40 years, the intrinsic invariant theory of conformal manifolds has been (more or less) completed; however, the problem of the extrinsic invariant theory - the conformal invariant theory of submanifolds embedded into a conformal manifold - is still incomplete. While much work in the last three decades has gone towards understanding the hypersurface case, higher codimensions have largely been neglected. In (ongoing) joint work with Josef Šilhan, we have produced a new method of proliferating conformal submanifold invariants using Gram matrices and the so-called tractor calculus of conformal geometry. In this talk, I will briefly introduce conformal geometry and the tractor calculus, I will discuss the motivating case of conformal hypersurfaces, and I will provide an outline of the new method.

14:30-15:30

Eivind Schneider (UiT)

Recurrent Lorentzian Weyl manifolds

We find the local form of all non-closed Lorentzian Weyl manifolds with recurrent curvature tensor. We then compute their differential invariants with respect to the pseudogroup of coordinate transformations preserving this local form, and thereby solve the local equivalence problem for generic non-closed Lorentzian Weyl manifolds with recurrent curvature tensor. While generic Weyl manifolds studied here have cohomogeneity two, there are some that have cohomogeneity 1 and 0, and we classify those. The relationship between recurrent Weyl structures and Einstein-Weyl structures is also discussed. This talk is based on joint work with Andrei Dikarev and Anton Galaev.