Friday 5.00-5.25 pm,  ROOM 129
Peter Hamburger (WKU, head) A Taste of Some Mathematical Arts
The authors illustrate how simple algebraic and geometric operations such as repeated multiplication and repeated rotations can create wonderful artistic images. They use one, two, and three dimensional animations to explain these mathematical methods and the rich arts behind them. They focus on 2D and 3D animation using prime number rotations of a simple, closed, planar curve about a given point to create the most stunning diagrams. This is a joint work with Edit Hepp artist and Richard Wartell undergraduate student.

Friday 5.25-5.30 pm,  ROOM 129   Welcome by Dean Blaine Ferrell

Friday 5.30-6.30 pm,  ROOM 129
Dr. Bart de Smit (Universiteit Leiden) Escher and the Droste effect - invited talk

One of M.C. Escher's most intriguing works depicts a man standing in a gallery who looks at a print of a city that contains the building that he is standing in himself. This picture, with the title Print Gallery, contains a mysterious white hole in the middle.

In a paper of Hendrik Lenstra and the speaker in the April 2003 issue of the Notices of the AMS it is shown that well known mathematical results about elliptic curves imply that what Escher was trying to achieve in this work has a unique mathematical solution. This discovery opened up the way to filling the void in the print. With help from artists and computer scientists a completion of the picture was constructed at the Universiteit Leiden. The white hole turns out to contain the entire image on a smaller scale, which in the Dutch language is known as the Droste effect, after the Dutch chocolate maker Droste.

In the talk the mathematics behind Escher's print and the process of filling the hole will be explained and visualized with computer animations.

Friday 6.45-7.05 pm

ROOM 129 • Barry Brunson (WKU) Mathematica and Art
Mathematica's "official description" is as a "system for doing mathematics by computer."  This brief talk will introduce and discuss some of the capabilities that  Mathematica offers for doing art and, perhaps, music by computer.

ROOM 125B • W. Todd Ashby (Charleston Southern University) A Proof of the Euler Identity
A proof (without using series) of the Euler Identity e^(ix)= cosx + isinx. This proof is from a paper that Euler wrote about logarithms of negative numbers in about 1747.

ROOM 125C • Lesley W. Wiglesworth (University of Louisville) A characterization on a class of unit bar-visibility graphs
Graphs that can be represented in the plane with horizontal bars corresponding to vertices and vertical bands of visibility between the bars corresponding to edges are called bar-visibility graphs (BVGs). They have been studied with applications to circuit design. BVGs were characterized in the mid-1980s, and polynomial time algorithms have been given to test whether a graph is a BVG and, if so, to provide a bar-visibility layout of the graph. However, these algorithms often produce bars with great differences in length. A unit bar-visibility graph (UBVG) is a bar-visibility graph in which all bars have the same unit length. A characterization of UBVGs has not yet been found, though certain classes of graphs have been characterized.  In this talk, a characterization of unit bar-visibility graphs that have a unit-bar layout with width less than two will be provided.

Friday 7.10 -7.30 pm

ROOM 129 • Dominic Lanphier (WKU) Symmetry, Escher, and on to sums of divisors
Symmetry can be indicative of an underlying group structure. The symmetry apparent in many of the works of M.C. Escher give tilings of the hyperbolic plane and there is an action of the modular group on such objects. From these beginnings, we can develop functions on the hyperbolic plane that "live" on such tilings. Such functions have deep arithmetic properties. 

ROOM 125B • Kelly Funk* (University of Louisville) A Generalization of Ceva and Menelaus’ Theorem
Ceva's Theorem and Menelaus' Theorem are two classic theorems in projective geometry that allow us to determine the concurrency of lines and collinearity of points of a triangle respectively.  In this talk we will consider a triangle in a projective plane over an arbitray field of characteristic not equal to two.  The results of Ceva and Menelaus will be included as special cases.

ROOM 125C • Mandy Smith* (Centre College) Invariants in Computer Vision
This research is focused on the problem of classifying curves up to rotations and translations with application to automated solving of an apictoral jigsaw puzzle. Two different methods are studied. The first, a more classical method based on differential invariants, produces a signature as a plot of curvature versus its derivative with respect to arclength. The second method involves using integral invariants to construct signatures. We study integral invariants from both theoretical and computational perspectives. We prove that integral invariants classify curves up to rotation and translation. We also code numerical approximations and experiment with integral signatures. The advantage of integral invariants over the differential invariants is that the integration reduces the effect of noise whereas differentiation amplifies it. We conduct numerous experiments verifying advantages and disadvantages of the differential and integral signatures.

Friday 7.35-7.55 pm

ROOM 129 • Curtis Palmer (Synergetic Design Inc.) LM Entropy my dear! What’s on?
A general systems view of ‘The Science of Art’ will be proposed and ‘The Art of Science’ will be explored with examples from the ‘Spline Mine’, computer generated transformations of polyhedra in projection.

ROOM 125B • John LaGrange* (The University of Tennessee) Zero-divisor graphs and Boolean rings
Let R be a commutative ring with 1 not equal 0. The zero-divisor graph of R is the (undirected) graph whose vertices are the nonzero zero-divisors of R, such that distinct vertices x and y are adjacent if and only if xy=0. In this talk, we shalldiscuss some of the fundamental properties possessed by zero-divisor graphs. Moreover, an exposition regarding the interplay between Boolean algebra, ring, and graph theoretic concepts will be given.

ROOM 125C • Qianyu Yang* (Centre College) Patterns in the Doubling Orbit of Koblitz Curves
In this talk, we show an interesting connection between cyclotomic cosets and doubling orbits of Koblitz Curves, a special class of elliptic curves.

Friday 8.05-8.25 pm

ROOM 129 • Bruce Kessler (WKU) Don't Believe Everything That You See
This talk will examine how the human brain interprets images, and does not always get things right. Mathematics and Mathematica will be used to generate several images and animations that simply "can not be right". This talk should be very accessible to a wide audience, and should be more visual than equation-al.

ROOM 125B • Ken Dutch (Eastern Kentucky University) Isoclines and Interference: A Geometric Approach to Bivariate Distributions
Many important practical problems about concordance of two random variables rely on having a more throrough understanding of the bivariate distribution than is afforded by simply computing the correlation.  In this talk we will discuss a portable geometric approach based on study of the isoclines.  After showing how this can be used to understand and compare some specific bivariate data sets, we will indicate how these techniques have been used to motivate solutions to several types of restricted inequality problems (problems where one seeks to improve the generic Fréchet–Hoeffding inequalities when additional information about the bivariate distribution has been given).  Most of this talk will be accessible to students who have taken or are taking a course in mathematical statistics.

ROOM 125C • Leah Campbell* (Centre College) Moving Toward Computerized Tutoring
Our research was part of a project to advance a computerized assistant for mathematics tutors. Our work was in the areas of computational linguistics and mathematics education. In the former, we isolated phrases in student-tutor dialogues that referred to equations being discussed by the student and tutor. We then wrote a parser to isolate the terms being referred to in the equations in an effort to link the dialogue phrases with the equation terms they referred to. In the mathematics education area, we identified and categorized student errors during tutoring sessions in an effort to determine the most common types of errors. By understanding the what types of errors occur most frequently, the computer will better know how to respond when a student reaches that error. The purpose of this research is to allow the computerized tutoring assistant to monitor the student-tutor conversation and automatically offer appropriate suggestions to the tutor when the student is stuck.

Friday 8.30-8.55 pm

ROOM 129 • Andrew T. Wilson (Austin Peay State University) So you want to be a Mathemagician?
I will demonstrate some magic tricks that can be explained using very basic mathematical concepts.

ROOM 125B • David Neal (WKU) Non-Equally-Likely Binomial Strings:  Does P(WWWLL) = P(LLWWW)?
Strings of wins and losses are generated from independent Poisson distributions. Given n occurrences through time t, the conditional distribution of the number of wins is analyzed to show that strings with the same numbers of wins and losses may not be equally likely.

ROOM 125C • Jacob Baxley* (WKU)  Erdos: Number Love
I will be discussing the fascinating life of the mathematician Paul Erdos. The interesting proof of the Erdos-Mordell inequlality will be presented, too. I thank Dr. Benko for his help and encouragement.

Saturday 8.30-8.50 am

ROOM 129 • CC Edwards (WKU) Farey Addition
Some people who don’t know how to add fractions erroneously add the numerators and add the denominators as in a/b + c/d = (a + c)/(b + d). This style of “adding” fractions is called Farey addition, and, although it is not the proper way of adding fractions, it does have legitimate applications in mathematics, as you will see in this talk.

ROOM 125B • Jillian Daniels* (WKU) The Beauty of the Golden Ratio
The golden ratio can be find in the nature, in art and in mathematics. All these will be demonstrated. I thank Dr. Benko for helping me with the math part of the talk.

ROOM 125C • Nicholas Johnson* (WKU) Maximum Modulus Principle of Complex Function
In the first part of the talk, we introduce different versions of  the Maximum Modulus Principle of Complex Function (MMP). Next, as applications, we use the MMP as a tool to solve several problems, including Schwarz's Lemma.

Saturday 9.00-9.20 am

ROOM 129 • David Benko (WKU) The Cons and Cons of Ebay
We will present the best buying and selling strategies on Ebay - from a mathematical point of view. We will also discuss why one should be cautious when buying things on Ebay. Disclaimer: I do not own shares of Ebay.  :)

ROOM 125B • Christopher McMahan* (WKU) A Variation in Thought about Delta Optimization
We introduce an application of the delta version of calculus of variations on time scale. The application will be made to a dynamic model of adjustment whose optimized solution can be obtained using the classical calculus of variations and/or the discrete calculus of variations. A comparison will then be made between the traditional methods of solution and the solution obtained using the delta version of calculus of variation on time scale. This paper will give merit to the real world application of the delta version of calculus of variation to such fields as economics, contrary to previously held assumptions. This is joint work with F. Atici.

ROOM 125C • Ben Ntatin (Austin Peay State university) Complex Homogeneous Spaces Under the action of a Real Lie Group
We discuss some examples of complex homogeneous spaces X=G/H with a connected real Lie group of holomorphic transformations acting transitively on X. Applications of the techniques used will include calculating the automorphism group of some bounded domains in C^n and parametrizing some maximal compact complex subvarieties.

Saturday 9.25-9.45 am

ROOM 129 • James Mai (Illinois State University) Square Expressions of the Golden Section: Compositional Strategies in the Paintings of James Mai
Golden Section geometry has provided the compositional structure for the paintings of artist James Mai for over 22 years. Mai's square paintings are subdivided by the Golden Ratio, which generates a framework of consistent angles and proportions across all compositional scales.  This coherent and flexible geometry has yielded a rich variety of compositional possibilities in Mai’s abstract work, ranging from symmetric and self-similar configurations to color interactions to spatial illusions.  This presentation offers both an overview of Mai’s art and a deeper analysis of selected paintings and their uses of the Golden Section.

ROOM 125B • Andy Martin (Kentucky State University) Is the Usual Linear Continuum a Good Model for the Real Numbers?
If a countable set of intervals, each of nonzero rational length, is defined so that each rational number is the center of one such interval, could their union fail to be the entire real line? We will show that the answer is yes, and discuss this paradoxical result.

ROOM 125C • Nick Hoffman* (Northern Kentucky University) How Injective are Hidden Field Equations?
Hidden Field Equation (HFE) is a public key cryptosystem.  HFE looks forward to a post-quantum world where the number theoretic public key cryptosystems – RSA, ElGamal, and ECC – are no longer secure. HFE encrypts using multivariate polynomials, but polynomials need not be injective. Therefore, decryption could be a problem.  We examine how injective hidden field equations are.

Saturday 9.50-10.10 am

ROOM 129 • Adam Coffman (Indiana University - Purdue University Fort Wayne) Parabolas in Space
In this expository talk, I will present parametric equations for parabolic curves in three-dimensional space and then generalize to surfaces in space containing many parabolas.   I'll use computer graphics to illustrate a classification theorem of Peters and Reif for quadratically parametrized surfaces, and explain the connection to my work on Steiner surfaces.

ROOM 125B • Bela Csaba (WKU) Metric spaces and probabilistic trees
Finite metric spaces play a fundamental role in many optimization problems. Finding the optimal solution in such metric spaces is sometimes computationally hard or even intractable. Therefore, approximate solutions are welcome. One possibility is to approximate the space by a set of "probabilistic trees". While in general these trees can have an intricate structure, we will demonstrate that for certain symmetric spaces (torus, Sierpienski's triangle, etc.) they have a nice description.

ROOM 125C • Kim Meyer* (University of Louisville) Complex Analysis and Dynamics of Polynomial Hele Shaw Cells
In this talk, I will discuss a fluid flow in varying regions. In particular, we are interested in the effect that suction or injection of fluid has on the free boundary. One may think of this as oil being sucked from the ground by an oil rig. This setup is known as a Hele Shaw Cell and is modeled mathematically by the so-called Polubarinova-Galin equation. We will discuss the development of this equation from Complex Analysis and present some explicit polynomial solutions to this equation. Finally we will discuss some open questions related to this model and look at how it can be applied in the future to planar biological structures and to the medical field.

Saturday 10.25-11.25 am,  ROOM 129

Dr. Stan Wagon (Macalester College, St. Paul, Minnesota) Frozen Math: Sculpting Interesting Surfaces in Snow - invited talk

Since 1999 I have organized a team to compete at the Breckenridge International Snow Sculpture Championships. We have chosen mathematical and geometrical themes for our work and have had good success, with seven awards in eight years at this international competition. In this talk I will show how one goes about the extremely satisfying task of carving a smooth and complicated surface from a 20-ton, 12-foot-high block of compacted snow. This beautiful white material puts special demands on the design team since snow is not all that strong and can melt. But under the right conditions -- cold -- it is indeed strong and yields a wonderful medium for learning about both sculpting technique and the mathematics of some intriguing geometrical shapes. The designers of the shapes we have carved have been Helaman Ferguson, Robert Longhurst, Bathsheba Grossman, Brent Collins, Carlo Séquin, and David Chamberlain.

Saturday 11.40-12.00 noon

ROOM 129 • Claus Ernst (WKU) Knots and Art
Knots have a long tradition in art. We can find knotted images of knots in paintings and as ornaments on buildings. A number of pictures of knots will shown that I consider beautiful. We will discuss some mathematical ideas of what makes a knot beautiful.

ROOM 125B • Jonathan Quiton(WKU): Graphical and Analytical Techniques for Outlier Detection and Goodness of Fit in the Recurrent Event Setting
This talk will first introduce what recurrent event data looks like and what type of models recurrent event data usually assume. Much of the talk will be focused on graphical and analytical ways of assessing whether a selected model is fits the data well enough, or whether there are some outlying observations that could adversely affect statistical inference. Examples using an engineering and biomedical recurrent event data will be given, and thoughts on possible collaborations and real-life applications will be discussed. This talk is taken from the author's phd Dissertation with Dr. Edsel A. Pena as research director.

ROOM 125C • Mark P. Robinson (WKU) Graphical Explorations of Global Behavior in Functional Iteration Problems
Functional iteration - the process of forming a sequence x0, x1 = f(x0), x2 = f(x1) =  f(f(x0)),... by repeated application of a function  f - is fundamental to the approximation of solutions to nonlinear equations and plays an important role in the study of nonlinear dynamics and chaos theory. In this talk, the particular aspect of functional iteration that is examined is the global behavior of the sequence f(x), f(f(x)), f(f(f(x))),... of composite functions as n increases without bound.    The use of computer graphics can be quite illuminating in enabling one to make conjectures which can then be investigated theoretically.

Saturday 12.05-12.25

ROOM 129 • Attila Por (WKU) Tillings and optimal dense packings
We will investigate tillings, a fundamental object in discrete geometry. Optimal packings of the plane (space) can lead to tillings of the given space.

ROOM 125B • Lance W. Hahn (WKU) Modeling Your Behavior with a Simple Computation
Empirical psychologists use a range of computational approaches to generate objective, well-defined predictions of human behavior. I will demonstrate a computational model for a free word association task. We will collect data from the audience and see how well our model predicts the results.

ROOM 125C • Zachary Rockrohr* (WKU) The 5th Letter
With the letter "e", I will talk about three topics about "e". The history, the concept taught to me by Dr. Benko and how to apply this into the world.

Saturday 12.30-12.50

ROOM 129 • Andre Wehner (Centre College) 300 Years of Euler
This year, we are celebrating the 300th birthday of the greatest 18th century mathematician, Leonhard Euler. This talk will be a historical overview over the many important contributions Euler made to all branches of classical mathematics and physics.

ROOM 125B • Melanie Autin (WKU) Modeling Periodicity in Estuarine Water Quality Data
Periodicity is omnipresent in environmental time series data.  For modeling estuarine water quality variables, harmonic regression analysis has long been the standard for dealing with periodicity.  Generalized additive models (GAMs) allow more flexibility in the response function, permitting parametric, semiparametric, and nonparametric regression functions of the predictor variables.  Harmonic regression, GAMs with cubic regression splines, and GAMs with cyclic regression splines are compared in simulations and using water quality data collected from the National Estuarine Research Reserve System (NERRS).

ROOM 125C • Robert T. Davis* (WKU) The Gruel-Graphical Applications of Duels
With art and entertainment in mind, we will look at an introduction to graph theory and its applications to the most extreme games of all Duels, Truels, and, Dr. Dominique Lanphier’s coined phrase, Gruels.  We will apply our new knowledge of graph theory to find out who should have won in the final showdown of The Good, The Bad, and The Ugly, as well as its applications to different sets of rules.

Saturday 12.55-1.15

ROOM 129 • Brett Bolen (WKU) Wormholes and Compactifing Extra Dimensions
One of the most interesting results in the late 1980's in General Relativity was the solution of traversable wormholes by Morse and Thorne. Unfortunately these solutions seem to require the use of so called "exotic matter". In this talk, I will examine if one can use compatifing extra dimensions to play the role of the exotic matter.

ROOM 125B • John Bryden (Austin Peay State University) A new idea in representation theory and its  application to the representation space of the braid groups
Recent work by Tyler Lawson has led to the construction of a spectral sequence that  relates the representation ring of an infinite discrete group G to its deformation  K-theory, which is basically the algebraic K-theory of a category obtained from the  unitary representations of the group G. If G=B_n, the n-string braid group then studying  the topological K-theory of BB_n gives enough information to apply Lawsons results to the  braid groups and obtain information about the homotopy type of the representation space  of B_n.

ROOM 125C • TBA

We gratefully acknowledge the funds which were provided for student travel by MAA NSF-RUMC (NSF Grant DMS-0241090, via the MAA) and Ogden College of Science and Engineering, WKU.