Self-similarity for Lie algebras Laurent Bartholdi (Goettingen) I will give the general definition of a self-similar Lie algebras: an algebra that contains "infinitesimal", tightly bound copies of itself, and show that important examples of Lie algebras fall into that class, in particular constructions by Petrogradsky, Shestakov and Zelmanov. In analogy with Burnside's problem, one is interested to understand infinite-dimensional algebraic algebra (every element generates a finite-dimensional subalgebra), and in particular nil algebras (every element raised to some power becomes 0). I will show that important such examples of algebra arise within self-similar Lie algebras, and will give sufficient conditions for a self-similar Lie algebra to be nil. I will also relate these self-similar Lie algebras to self-similar groups such as examples by Grigorchuk and Gupta-Sidki, and will also show their connection to Caranti's classification of algebras of maximal class.