A Prolog-assisted search for simple Lie algebras

par David Stewart (Université de Newcastle)

jeudi 17 nov. 2022, 11:15 → 12:15 Europe/Paris

salle Fokko du Cloux (ICJ (Braconnier))

This is joint work with David Cushing and George Stagg.

Prolog is a very unusual programming language, which was developed by Alain Colmerauer in one of the buildings on the way to the CIRM in Luminy. It is not fundamentally iterative in the way that, for example, GAP and Magma are. Instead it operates by taking a list of axioms as input, and responds at the command line to queries asking the language to achieve particular goals. It gained some notoriety by beating contestants on the game show Jeopardy in 2011. It is also the world's fastest sudoku solver. I will describe some recent Prolog investigations to search for new simple Lie algebras over the field GF(2). We were able to discover some new examples in dimensions 15 and 31 and extrapolate from these to construct two new infinite families of simple Lie algebras.