YONSEIMath-CSE Colloquium
2021. 10. 7. (목) 17 : 00
Geometry of Elie Cartan's “Pfaffian systems in 5 variables”
Elie Cartan's celebrated paper "Pfaffian systems in 5 variables" in 1910 studied the equivalence problem for general Pfaffian systems of rank 3 in 5 variables as the curved version of the Pfaffian system with G2 symmetry.
The G2 case admits a beautiful geometric correspondence with Engel's PDE system. We give a historical overview of Cartan's paper and discuss recent joint work with Qifeng Li, extending the correspondence to curved cases, which is based on ideas from geometric control theory and algebraic geometry.