Dennis The, The University of Tromso
"Exceptionally simple PDE"
Arguably one of the most beautiful results of 19th century mathematics was the classification of complex simple Lie algebras due to Cartan and Killing. Beyond the four classical families of matrix Lie algebras, five mysterious "exceptional simple" Lie algebras made their first appearance in this story. In 1893, the smallest of these, G2, was first realized by Cartan and Engel as the infinitesimal symmetries of various geometric objects. In this talk, I will review this story and discuss how it was recently generalized in a remarkably uniform manner to obtain analogous explicit geometric realisations for (almost) any complex simple Lie algebra.