Math Department Events Listing

A map is an embedding of a connected, labeled graph into a compact oriented surface such that the edges of the graph do not intersect and the complement of the graph is a disjoint union of open cells homeomorphic to the disk. These cells are called the faces of the map. In the case of genus zero one-face maps, the embedded graph is a tree. There are various methods of representing a genus zero one-face map. Connections between these representations and the map's embedded tree will be explored, and combinatorial properties of the tree discussed. In particular, we will explore connections between the distribution of vertex degrees, vertex adjacencies, and the spectrum of the embedded tree.

A standard technique for solving Diophantine equations is to factor them over the integer rings of appropriate number fields. Since this technique bears fruit typically only when this ring has the unique factorization property, one is immediately led to the question of whether or not a given number field can be embedded into a finite extension field with trivial class group. Answers to this question naturally lead us, via class field theory, to studying towers of number fields (Hilbert class field towers, among others) with amazing arithmetic properties. This talk will be a survey of the concepts and techniques, and the very few concrete results, arising from this line of inquiry.

Julia Arciero and Rebecca Vandiver (Applied Math), and Jose Gifford (Computer Science) , The University of Arizona, will speak on Structure, Function, and Adaptation of Microcirculation: Discussion/Critique.

I'll review the history of calculus reform: what we were trying to do, what we accomplished, and what is to be done in the future.

I discuss why we should require our students to write more in mathematics, and I'll provide some examples of the work I've done in this area.