Some applications require non-Riemannian spacetimes, such as Carrollian or Galilean spacetimes. They describe, respectively, ultra- and non-relativistic limits of gravity.
In my talk I construct the Newton-Cartan version of two-dimensional dilaton gravity, which plays essentially the same role for Newton-Cartan gravity as generic dilaton gravity does for Riemann-Cartan gravity.
https://arxiv.org/abs/2011.13870
https://univienna.zoom.us/j/6540036841?pwd=SytyVkZJZzNyRG9lMm13ejlHeHRRUT09