Dave Witte Morris, University of Lethbridge, Canada
Colloquium Title: What is a superrigid subgroup?
Abstract: In combinatorial geometry (and engineering), it is important to know that certain scaffold-like geometric structures are rigid. (They will not collapse, and, in fact, have enough bracing that they cannot be deformed at all.) Replacing the geometric structure with an algebraic structure (namely, a group) leads to the following question: given a homomorphism that is defined on the elements of a subgroup, is it possible to extrapolate the homomorphism to the rest of the elements of the group? It is fairly obvious that every additive homomorphism from the group ℤ of integers to the real line ℝ can be extended to a homomorphism that is defined on all of ℝ, and we will see some other examples.