Geometric group theory seminar - 2017/18

The seminar meets each Wednesday at 3 PM in BURN 920

McGill GGT research group

Upcoming talks:

September 6, 2017: Stéphane Lamy (Université Paul Sabatier), Signature morphisms on the Cremona group.

The Cremona group is the group of birational symmetries of the plane. This is a rather huge group, which is neither finitely generated nor finite dimensional. The abelianization of the Cremona group was recently studied: over the base field C, the abelianization is trivial, but over R, the abelianization is an uncountable direct sum of Z/2. I will discuss similar results over more general fields, such as number fields or finite fields. The key is to use a natural action on a square complex, to exhibit various trees as quotients or subcomplexes, and then to apply Bass-Serre theory (joint work with Susanna Zimmermann).

September 27, 2017: Sang-hyun Kim (Seoul National University), Free products in Diff(S1).

We prove that if G is a finitely generated non-virtually-abelian group, then (G x Z) * Z does not embed into Diff^2(S^1). In particular, the class of subgroups of Diff^r(S^1) is not closed under taking free products for each r >= 2. We complete the classification of RAAGs embeddable in Diff^r(S^1) for each r, answering a question in a paper of M. Kapovich. (Joint work with Thomas Koberda)

Seminar schedule archive