Undergraduate honors thesis defense

Title: Spaces of Orders on Magmas
Speaker: Paul Bianco
Date and Time: Friday, December 13, 11am
Place: Phillips Hall, Room 736

Abstract: A left ordering of a magma (a set with a binary operation) is a total order that is left-invariant under the operation. There is a natural topology on the space of these orders, which has been well studied. These spaces are of interest to both algebraists and topologists, and in the countable case to computability theorists as well.

Each space can be embedded into some Cantor cube {0,1}^tau. For free abelian groups of countable rank at least 2, this space is known to be homeomorphic to the Cantor set {0,1}^omega, but little work has been done on uncountable magmas. We show that for a free abelian group of any rank, the space of orders is homeomorphic to a Cantor cube.

Faculty adviser: Valentina Harizanov

Everyone is invited to attend.