Séminaire Géométrie et groupes discrets

Milnorian and non-Milnorian Representations

by Prof. Ilia Smilga (Yale University)

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons



In 1977, Milnor formulated the following conjecture: every discrete group of affine transformations acting properly on the affine space is virtually solvable. We now know that this statement is false; the current goal is to gain a better understanding of the counterexamples to this conjecture. Every group that violates this conjecture "lives" in a certain algebraic affine group, which can be specified by giving a linear group and a representation thereof. Representations that give rise to counterexamples are said to be non-Milnorian. We will talk about the progress made so far towards classification of these non-Milnorian representations.