The Slow Pitch talks will take place on Wednesdays at 4, unless otherwise noted. Tea and cookies or other food will be served 15 minutes before the talk starts. The talks should be aimed at both undergraduate and graduate students in mathematics. Students, both undergraduate, gradute, and faculty are encouraged to give talks. Topics can be vary widly. Some topics include (but are not limited to): algebra, logic, set theory, probability, analysis and geometry. To sign up to give a talk, pick an open date below and email Nic Flores at Nicandro.Flores@colorado.edu or Ilia Mishev at Ilia.Mishev@colorado.edu.
Spring 2007 Schedule
Wednesday, April 11th @ 4pm in Math 350
Who: Peter Mayr
Title: Slow Clones (Functions on Algebras)
Abstract: An algebraic structure (algebra) consists of a set of elements (e.g. the integers) together with basic operations (e.g. addition,multiplication). A natural way of classifying algebras is by considering the set of all functions -- the so-called clone that can be built from the respective basic operations using composition. Algebras on the same set of elements are said to be equivalent if their clones are equal. For example, on the 2-element set the Boolean algebra and the Boolean ring are equivalent since in both cases the basic operations generate all Boolean functions. I will talk about results and problems on clones and explain how methods from group theory can be applied to study more general algebras.
Wednesday, April 25th @ 4pm in Math 350
Who: Jason Hill
Title: Finding Totally Real Quintic Number Fields of Minimal Signature Group Rank
Abstract: This talk relates to my current research with Dave Dummit at The University of Vermont and is intended to be generally understandable by those who have completed or are close to completing Algebra 2. The topic area is 'algebraic and algorithmic number theory.'
The basic idea is as follows: Consider an extension of degree 5 over Q generated by a quintic with five real roots. The units of such a field are known to have a particularly nice structure by a theorem of Dirichlet, in fact they are finitely generated and in R. However, to properly formulate a conjecture of Stark, we wish to determine if it is possible to construct such a field where no unit generator ever changes sign under any of the field's Galois embeddings. Before this work, no field at all close to having this property was known. It was conjectured by some that such a field could not exist and claimed by others that such a field does exist. In this talk, I will prove which side is correct.