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- Department of Mathematical Sciences Seminars & Workshops Archive 2009-10

**Colloquium**

- Lyn English, Queensland University of Technology, Brisbane (Australia).
*Complex Learning in Interdisciplinary Contexts*.- Professor Lyn English is internationally recognized for her extensive research and publications in mathematics education, which has spanned preschool through to year 10. Her areas of research include mathematical modelling in the primary school, problem solving and posing, statistical reasoning, analogical reasoning, early mathematical development, and web-based distributed learning communities. Prof. English's new field of research is engineering education in the middle and primary school, involving collaborative work with staff from QUT's School of Urban Development and Purdue University's Institute for P-12 Engineering Research and Learning, where she is a member of the Institute's advisory board. Prof. English is a Fellow of the Academy of the Social Sciences in Australia. She is founding editor of the international journal
*Mathematical Thinking and Learning*, which is published by Taylor & Francis in the US. Prof. English is on the editorial board of several international journals including*Contemporary Educational Psychology*,*The International Electronic Journal of Mathematics Education*, and*Educational Sciences: Theory & Practice*.

- Professor Lyn English is internationally recognized for her extensive research and publications in mathematics education, which has spanned preschool through to year 10. Her areas of research include mathematical modelling in the primary school, problem solving and posing, statistical reasoning, analogical reasoning, early mathematical development, and web-based distributed learning communities. Prof. English's new field of research is engineering education in the middle and primary school, involving collaborative work with staff from QUT's School of Urban Development and Purdue University's Institute for P-12 Engineering Research and Learning, where she is a member of the Institute's advisory board. Prof. English is a Fellow of the Academy of the Social Sciences in Australia. She is founding editor of the international journal
- Subramanian Arumugam, Kalasalingam University (India).
*Distance Magic Graphs*.- Abstract: A graph
*G*with*n*vertices is called*distance magic*if its vertices can be labeled with the numbers 1, 2, … ,*n*in such a way that the sum of the numbers assigned to the neighbors of a vertex is always the same. In this talk, we survey the literature on distance magic graphs, and then present some of our recent results, open problems, and conjectures.

- Abstract: A graph

- Garret Marshall, IPFW graduate student,
*Longitudinal Data Analysis*. - Matt Walsh,
*Harmony and Compromise: The Math Behind Musical Scales*. - Allen Schwenk, Western Michigan University,
*What Does 'Mean' Mean?*

**Discrete Math Seminar**

- Matt Walsh,
*Binary base-phi representations of positive integers* - Doug Weakley,
*Is every C-infinity word recurrent?* - Marc Lipman,
*Complete sphere-of-influence graphs*. - Chip Vandell,
*Connected decycling in hypercubes.* - Marc Lipman,
*Highly-connected networks with low degree*.

**Analysis Seminar**

- Peter Dragnev,
*Ping pong balayage and convexity of the Riesz and logarithmic equilibrium measures*.- Abstract: Let
*E*be the union of finitely many intervals or arcs on the unit circle. In joint work with David Benko we prove that the equilibrium measure of*E*has a convex density. This is true for both the classical logarithmic kernel, and the Riesz kernel. The electrostatic interpretation is the following: if we have a finite union of subintervals on the real line, or arcs on the unit circle, the electrostatic distribution of many "electrons" will have convex density on every subinterval. I will present applications of this result to external field problems and constrained energy problems.

- Abstract: Let

**Colloquium**

- Erwin Mina-Diaz, University of Mississippi,
*Asymptotics of Polynomials Orthogonal on the Unit Disk with respect to a Positive Polynomial Weight*, Aug. 11.- Abstract: We derive asymptotics for polynomials orthogonal over the complex unit disk
*D*= {*z*: |*z*| < 1} with respect to a weight of the form |*h*(*z*)|^{2}, with*h*(*z*) a polynomial without zeros in*D*. The behavior of the polynomials is established at every point of the complex plane.

- Abstract: We derive asymptotics for polynomials orthogonal over the complex unit disk
- N. Rao Chaganty, Old Dominion University,
*Multivariate Discrete Models Based on Copulas for Repeated Measurements*. June 3.- The multivariate normal distribution is often used in the modeling and analysis of repeated measurements such as clustered and longitudinal data. While the multivariate normal distribution can simplify analysis in the continuous case, no corresponding multivariate distribution analogue has been commonly accepted for discrete variables such as binary, count or ordinal variables. The use of copulas for modeling multivariate discrete responses is seen as a promising solution. Specifically, exchangeable copulas can be used to model clustered discrete data, while longitudinal discrete data can be modeled by an appropriate copula with decreasing time-lag dependence. The specification of the multivariate discrete distribution through the use of copula functions provides complete inference, in the sense that maximum likelihood estimation and the calculation of joint and conditional probabilities are possible. In this talk, I will provide a concise introduction to copulas and discuss various methodologies for parameter estimation.

**Colloquium**

- Yu Yan, Huntington University,
*The Scalar Curvature Deformation Equation on Locally Conformally Flat Compact Manifolds*. April 28. - Natalia Zorii, Institute of Mathematics, National Academy of Sciences of Ukraine,
*Equilibrium Problems for Infinite-Dimensional Vector Potentials with External Fields*. May 14.

** Analysis Seminar**

- Peter Dragnev,
*Asymptotic behavior of Carleman orthogonal polynomials*. - Adam Coffman,
*Glaeser's Inequality on an Interval*.

**Pi Math Club**

- Student talks: Cynthia Ellis,
*Origami: More than an art form*; and Cindy Harter,*A tale of transitivity*. - Lunchtime talk: Paul Richeson (IPFW student and intern at Lincoln Financial), and Rick Richmond, FSA, MAAA (actuarial consultant at Lincoln Financial),
*Becoming an Actuary*. - D. Maloney, IPFW Physics,
*Problems and Problem Solving Tools*.

**Pi Mu Epsilon**

- Adam Coffman,
*Möbius transformations and ellipses*.

**Colloquium**

- Johann S. Brauchart, Vanderbilt University,
*Weighted Minimal Energy Problem on the Unit Sphere*. Aug. 28.- Consider an isolated charged sphere in the presence of an external field exerted by a point charge over the North Pole. Point charges are thought to interact according to the Riesz
*s*-potential 1 /*r*^*s*with*d*-2<*s*<*d*. (Here,*d*+1 is the dimension of the embedding space.) We present results from joint work with Peter Dragnev and Ed Saff concerning the weighted extremal measure solving this external field problem and its properties (support, representation, potential).

- Consider an isolated charged sphere in the presence of an external field exerted by a point charge over the North Pole. Point charges are thought to interact according to the Riesz
- N. Rao Chaganty, Old Dominion University,
*Analysis of Clustered and Longitudinal Binary Data*. Sept. 4.- Clustered and longitudinal binary data occur in genetics, biomedical, and a wide range of scientific studies. These data are naturally dependent, and common measures of association for the study of dependence between the binary variables include correlations and odd ratios. In this talk I will discuss permissible ranges of these measures of association. I will present some examples to show that the generalized estimating equations method, a nonlikelihood and moment based method, ignores these ranges and gives misleading
*p*-values and incorrect conclusions. A proper likelihood approach for the analysis of dependent binary, and in general discrete, data is based on copulas. If time permits, I will give a short introduction to copulas as well.

- Clustered and longitudinal binary data occur in genetics, biomedical, and a wide range of scientific studies. These data are naturally dependent, and common measures of association for the study of dependence between the binary variables include correlations and odd ratios. In this talk I will discuss permissible ranges of these measures of association. I will present some examples to show that the generalized estimating equations method, a nonlikelihood and moment based method, ignores these ranges and gives misleading

**Pi Math Club**

- G. Petruska, IPFW Computer Science,
*Series and Products: Euler's Wizardry*.- The main topic of this talk will be Euler's famous summation formula (also known as the Euler-Maculaurin formula). Following Euler's path, we will deduce several interesting results, some of which go back centuries into the history of mathematics. Understanding the mathematical thinking and machinery of Euler's era, we will endeavor to apply these results to "obtain" more modern results, such as the famous Mertens' theorem.

**Colloquium**

- Debraj Chakrabarti, University of Notre Dame,
*CR Functions on Singular Hypersurfaces*.- We consider the question: which functions on a hypersurface
*M*in^**C***n*(*n > =*2) arise as the boundary value of holomorphic functions? When*M*is smooth, the answer to the global version of this question is that the function on*M*is CR (Bochner-Hartogs theorem.) There are however obstructions to local extension of CR functions (non-minimality). We consider the local problem for a class of singular hypersurfaces (which includes the real analytic singular hypersurfaces) and describe some new phenomena which can occur only in the singular case.

- We consider the question: which functions on a hypersurface
- David Benko, University of South Alabama,
*The Integrity of Graphs*.- The integrity of a graph is a certain number which measures how difficult it is to break the graph into small components. This is a useful number to consider when designing networks. We calculate the integrity of "box-graphs" in dimension
*d*(up to a constant factor). We also give an upper estimate on the integrity of planar graphs. Joint work with C. Ernst and D. Lanphier.

- The integrity of a graph is a certain number which measures how difficult it is to break the graph into small components. This is a useful number to consider when designing networks. We calculate the integrity of "box-graphs" in dimension

**Analysis Seminar**

- Adam Coffman,
*CR singularities of real 4-manifolds in***C**^{3}*, part III.*

**Pi Mu Epsilon**

- John LaMaster,
*The fourth dimension*.

**Pi Math Club**

- Student Research Talks:
- Garret Marshall,
*The confessions of tortured data* - Richard Grzych,
*Relax, problem solved* - Ryan Fritz and Chris Baber,
*How financial indicators compare with an economic indicator*

- Garret Marshall,
- L. Beineke, IPFW,
*Through the Lurking Graphs*.- Behind many a game and puzzle there lies some graph theory. In this presentation, we will give some of the ABCs of the subject, such as Asteroid, Bridg-it, Curious Coins, and Dots-and-Boxes (and more). The talk will be accessible to students without a background in graph theory.

- Peter Dragnev,
*School Districts on Mars, Fuel Depots on Jupiter, Inimical Dictators on Neptune?! Or How to Arrange Points on the Sphere*.- Isn’t it interesting what connects the objects in the title? Wouldn’t it be wonderful if all Schools were so perfectly located on Mars that no students in any School District had to walk “too much”? Or the Fuel Depots were so conveniently located that it was easy to ship fuel to all parts of Jupiter? And what about all these Dictators on Neptune, that hate each other so much, that we want them as far apart as possible?

Now seriously, the “uniform” distribution of many points on the unit sphere is a highly non-trivial problem with applications throughout the whole spectrum of modern science. Whether one studies electrons in equilibrium from Physics, large fullerene compounds from Chemistry, orifices of pollen grain from Biology, or data encoding from Computer Science, one arrives at spherical arrangements of points that minimize some form of energy. So, tighten your seatbelts and prepare for a fascinating journey around the Galaxy of Minimal Energy Points.

- Isn’t it interesting what connects the objects in the title? Wouldn’t it be wonderful if all Schools were so perfectly located on Mars that no students in any School District had to walk “too much”? Or the Fuel Depots were so conveniently located that it was easy to ship fuel to all parts of Jupiter? And what about all these Dictators on Neptune, that hate each other so much, that we want them as far apart as possible?
- Drew Swartz, IPFW undergraduate math major
*, An Investigation of the Structure Underlying Irreducible Divisors.*- Interested in learning about a current area of mathematical research? This talk will discuss some of the work being done by undergraduates, like yourselves, at an undergraduate research program at Wabash College, funded by the National Science Foundation. Don't be deterred if you have not yet had a course in Abstract Algebra. Plenty of time will be allocated towards giving a general introduction to the topics at hand.

A current trend in algebraic research is to utilize graph theory as a tool to analyze the algebraic properties of special sets of numbers, called "rings." In this talk we'll examine how the relatively new concept of the "irreducible divisor graph" allows us to better understand factoring within rings.

- Interested in learning about a current area of mathematical research? This talk will discuss some of the work being done by undergraduates, like yourselves, at an undergraduate research program at Wabash College, funded by the National Science Foundation. Don't be deterred if you have not yet had a course in Abstract Algebra. Plenty of time will be allocated towards giving a general introduction to the topics at hand.