Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"
sala 106 IM PAN, ul. Śniadeckich 8, Ip
2018-03-21 (14:15) 
Katja Sagerschnig (University of Vienna)
The Geometry of Almost Einstein (2,3,5) Distributions
The first part of the talk will be a brief introduction to Cartan geometries related with the exceptional Lie group G2, i.e., to (2,3,5) distributions and to contact twisted cubic structures. I will introduce the associated normal Cartan connection, and an equivalent concept, the normal tractor connection. I will also recall Nurowski's construction of a conformal structure associated with a (2,3,5) distribution.
The goal of the second part is to explain joint work with Travis Willse on the geometry of Nurowski conformal structures admitting parallel standard tractors. Such a parallel tractor determines a partition of the manifold into several submanifolds, each naturally endowed with a geometric structure. This will reveal links between (2,3,5) distributions and several other geometries, including, Sasaki-Einstein structures of signature (2,3), Fefferman-conformal structures, and their para-complex analogues.I will also relate this picture to work of Gil Bor, Pawel Nurowski andOmid Makhmali.
The goal of the second part is to explain joint work with Travis Willse on the geometry of Nurowski conformal structures admitting parallel standard tractors. Such a parallel tractor determines a partition of the manifold into several submanifolds, each naturally endowed with a geometric structure. This will reveal links between (2,3,5) distributions and several other geometries, including, Sasaki-Einstein structures of signature (2,3), Fefferman-conformal structures, and their para-complex analogues.I will also relate this picture to work of Gil Bor, Pawel Nurowski andOmid Makhmali.