|University of South Carolina
|14h00 - 15h00
Finite subgroups of Cremona groups and representation dimension
The Cremona group of rank n is the group of birational automorphisms of n-dimensional projective space. Alternatively, the Cremona group of rank n is the group of automorphisms of a purely transcendental extension. Cremona groups are infamously large. In particular, even the plane Cremona group cannot be embedded into a linear algebraic group. Their finite subgroups are much more manageable, but still not completely understood even in the rank 2 case over the complex numbers. However, lacking a complete classification, one may attempt to find bounds for their complexity. Over a number field, one can consider the orders of the finite subgroups. Over general fields, there is the Jordan constant. I consider the minimal dimension of a faithful representation. This is joint work with B. Heath and C. Urech.