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 Josh Wiscons at wiscons@colorado.edu or Ilia Mishev at Ilia.Mishev@colorado.edu.
Fall 2007 Schedule
Wednesday, August 29th @ 4pm in Math 350
Who: Brian Rider and Nat Thiem
Title: An Introduction to the Random Matrix Theory and Algebraic Lie Theory Seminars
Abstract: Each Speaker will talk for appoximately 25 minutes about what one might encounter in the Random Matrix Theory and Algebraic Lie Theory seminars.
Wednesday, September 5th @ 4pm in Math 350
Who: Steve Preston
Title: An Introduction to the DE/Geo/Top Seminar
Abstract: The speaker will talk about what one might encounter in the Differential Equations/Geometry/Topology seminar.
Wednesday, September 12th @ 4pm in Math 350
Who: Josh Sanders
Title: The Basics
Abstract:
Why does math work? How do we know that we can believe a proof? How can we be so sure that
mathematical objects even make sense? One attempt to answer these types of questions lies in the
branch of mathematics now known as Foundations, which includes set theory and logic.
In this talk, I will discuss the most commonly accepted set of set theory axioms (the ZFC axioms), as well
as some not-so-commonly accepted axioms. I will also demonstrate a simple example of how you can
"do" much of mathematics within the framework of these axioms (Peano arithmetic via the ordinals), and
take this example even further (because we can). For anyone who has had a course in set theory or
foundations, much of this talk will be review; it will be accessible to anyone reading this (although I will
assume that you know... um... something about math.)
Wednesday, September 19th @ 4pm in Math 350
Who: Ilia Mishev
Title: An Introduction to the Poincare Upper Half-Plane
Abstract: I will talk about some of the basic results about the Poincare Upper Half-Plane H such as hyperbolic arc length, area, action of SL(2,R) on H, fundamental domain of SL(2,Z), the Laplacian operator and the hyperbolic Fourier transform on H.
Wednesday, September 26th @ 4pm in Math 350
Who: Troy Seguin
Abstract: Functional Analysis and Martingale Theory have recently played a major role in mathematically modelling financial markets. I will be discussing some of the mathematics and techniques used in these models as well as illustrating methods behind calculating stock option prices.
Wednesday, October 3rd @ 4pm in Math 350
Who: Ilia Mishev
Title: The Fourier Transform and Wavelets
Abstract: I will talk about the Fourier transform on R, some properties, the Heisenberg uncertainty principle, and then introduce wavelets on R and talk about how one might start constructing wavelets on the Poicare upper half-plane H.
Wednesday, October 10th @ 4pm in Math 350
Who: Dana Ernst
Title: The Temperley-Lieb Algebras of Types $A$ and $B$ and Their Associated Diagram Algebras
Abstract: The Temperley-Lieb Algebra, invented by Temperley and Lieb in 1971, is a certain finite dimensional associative algebra, which arose in the context of statistical mechanics. Later in 1971, Roger Penrose showed that this algebra can be realized as a certain diagram algebra. Then in 1987, V.F.R. Jones showed that the Temperley-Lieb Algebra occurs naturally as a quotient of the Hecke algebra arising from a Coxeter system of type $A$ (whose underlying group is the symmetric group). Eventually, this realization of the Temperley-Lieb Algebra as a Hecke algebra quotient was generalized to the case of an arbitrary Coxeter system. In this talk, we will introduce the diagram algebras corresponding to the Temperley-Lieb Algebras of Coxeter types $A$ and $B$. At the end of the talk, I will briefly discuss my current research on the Temperley-Lieb Algebra of type $\widetilde{C}$. This all sounds complicated, but I'll only assume that you know some basics about groups and vector spaces.
Wednesday, October 17th @ 4pm in Math 350
Who: Tim Schumacher
Title: The Trace Problem and Fractional Order Differentiation
Abstract: The need to study traces of functions arises naturally in boundary value problems and is an interesting subject in its own right. We will describe the trace problem and define some function spaces that provide very nice answers to it. The aim of the talk is to be an overview of the subject, stating the main results without proof.
Wednesday, October 24th @ 4pm in Math 350
Who: Vinod Radhakrishnan
Title: Equations over finite fields
Abstract: I will consider the problem of counting the number of solutions to equations over finite fields. We will work with specific examples and give illustrations of the Weil "conjectures", the Shimura-Taniyama "conjecture" (both proven) and the Birch-Swinnerton Dyer conjecture for elliptic
curves. Knowing a little bit about finite fields will be useful but not necessary. No knowledge of elliptic curves will be needed to follow the talk.
Wednesday, October 31st @ 4pm in Math 350
Who: Patrick Brown
Title: Bowling
Abstract: Are you better than the average bowler? That is, are your scores higher than the
average of all possible games? Is your score higher than the average of a
random bowler? What about a binomial bowler?
In this talk, we will derive an average for all possible games of bowling. We will also explore random bowling, in which all possible outcomes are equally likely
in a given roll, and binomial bowling, in which the pins fall according to a
binomial distribution, and derive an average for each.
Monday, November 5th @ 4pm in Math 350
Who: Chris Sinclair
Title: Polynomials with all roots on the unit circle
Abstract: The coefficients of polynomials with all roots on the unit circle display an amazing amount of geometric structure. We'll talk about the geometry of the set of these coefficient vectors, examine some implications in number theory and explore some connections with random matrix theory.
Wednesday, November 14th @ 4pm in Math 350
No Slow Pitch this week
Wednesday, November 21st @ 4pm in Math 350
No Slow Pitch this week
Monday, November 26th @ 4pm in Math 350
Who: Shawn Baland
Title: On the Classification of Finite-Dimensional Complex Simple Lie Algebras
Abstract: Lie algebras play a vital role in mathematical physics, the theory of differential equations, and the study of Lie groups. In this talk, I will introduce some elementary results in Lie algebra theory, along with a few motivating examples. I will then briefly outline the classification theorem for the finite-dimensional simple Lie algebras over the complex numbers. Along the way, we will encounter several structures that are used throughout Lie theory, including weight spaces, root systems, Cartan matrices, and Dynkin diagrams. A firm knowledge of linear algebra will be helpful, but not necessary.
Wednesday, November 28th @ 4pm in Math 350
Who: TBA
Title: TBA
Abstract: TBA
Wednesday, December 5th @ 4pm in Math 350
Who: TBA
Title: TBA
Abstract: TBA
Wednesday, December 12th @ 4pm in Math 350
Who: Nic Flores
Title: Counting Directed Acyclic Graphs and its application to Monte Carlo Learning of Bayesian Networks
Abstract: In recent years the problem of learning the structure of Bayesian Networks from
data has gained great interest. One way of learning Bayesian Networks from data is to
use an algorithm that steps through the state space of Directed Acyclic Graphs (DAGs) using
a type of random walk. In this talk I will present a counting formula that allows such algorithm
to move through the state space of DAGs with extreme efficiency.
Previous Slow Pitch Schedules
Spring 2007