|DATE||February 17 (Mon), 2020|
|HOST||Bhamidi, S.S Sreedhar|
|TITLE||[GS_M_3W] Three W's Seminar: On Cartan connections|
Riemannian manifolds are infinitesimally Euclidean. Likewise, one may think about geometries in which spaces are infinitesimally modeled on homogeneous spaces—Cartan connections are what describe them. In this talk, I’m going to discuss the naturalness of the idea of Cartan connections, putting some emphasis on the notion of development of curves, and explain what the Cartan connections describing Riemannian and conformal geometry are like. It is worth noting that the Weyl curvature tensor, whose vanishing characterizes the local conformal flatness, is best understood along this line of thought. I’m also planning to touch upon the relation of the conformal Cartan connection to the Fefferman-Graham “ambient metric” construction and to Poincaré-Einstein manifolds.