# Colloquia

**Future Colloquia**

**Future Colloquia**More colloquia coming soon!

**Past Colloquia**

**Past Colloquia****2016-2017**

**2016-2017**

** **

**Thursday, April 13, 2017 at 11:00 a.m. in Lytle Hall 214**

**"Connecting the Dots & Coloring Paths: Adventures in Graph Theory"**

**Dr. Karen McCready, King's College **

In this talk we will look at some basic properties of graphs as well as some classical problems that arise in the study of graph theory. We will also consider a modification of the diameter of a graph for edge-colored graphs, called the proper diameter, which is a function of both the graph and its coloring. This will lead us to explore the relationship between the diameter and proper diameter of certain graph classes.

**Tuesday, February 14, 2017 at 3:00 p.m. in Lytle Hall 214**

**"Fluid Limit for a Batched Processor Sharing Queue"**

**Ms. Katelynn Kochalski, University of Virginia**

In queueing theory we refer to the items in the queue as jobs and the rule that dictates how jobs are processed as the service policy. A common service policy is First-In-First-Out (FIFO). In FIFO, the job that has been waiting in line the longest is served next. This is the service policy that is used in line at the grocery store or bank. We study a sequence of queues operating under a service policy where the system creates batches and works on multiple jobs at a time. Motivated by the law of large numbers from classical probability, we find a fluid limit for the queues. This limiting result provides a simple description for a complicated system. We can then use this simpler limiting object to approximate what happens in the system. In particular, we show the model is completely described by its initial state and each batch will start in a predictable, periodic way.

**Friday, February 10 at 3:00 p.m. in Lytle Hall 214**

**"Attack of the Tiny Titans"**

**Dr. Brooks Emerick, Trinity College **

This talk will discuss the mathematical modeling approach to describe the interactions of a host and a parasitioid a.k.a. tiny titan. A parasitoid is an organism that spends a portion of its life attached to or within a single host organism. Unlike a parasite, a parasitoid will eventually kill or consume the host. Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact allowing specific behaviors to be mechanistically incorporated. We'll introduce the traditional methods used and present results from models that include behaviors such as host-feeding, parasitoid migration, and variation of risk.

**Tuesday, February 7, 2017 at 3:00 p.m. in Lytle Hall 214**

**"From Theory to Practice: Boundary Value Problems and Prokelisia marginata"**

**Mr. Quinn Morris, UNC-Greensboro **

In a first course in ordinary differential equations, one often treats initial value problems of the form u'' + f(u) = 0, u(a)=u_0, u'(a)=u_1, and is able to show existence & uniqueness of such solutions when $f$ is ``nice." In this talk, we will instead consider boundary value problems of the form u'' + f(u) = 0, u(a)=u_0, u(b)=u_1, and observe that even for very "nice" functions f, we can get very exotic behavior. At the end of the talk, we will examine a boundary value problem from population dynamics which is of recent interest.

**Tuesday, January 31, 2017 at 3:00 p.m. in Lytle Hall 214**

**"Harmonic maps with repulsive potentials "**

**Ms. Lizzy Huang, Duke University **

Many questions in topology and physics can be expressed in terms of finding a function $f$ between a curved space $M$ (the domain) and another curved space $N$ (the target) which minimizes a natural energy functional: $\int_M |df|^2 dx$. Functions that minimize this energy are called harmonic maps. One method to obtain a harmonic map is to consider a family of maps $f_t$ which follow a path of `steepest descent.' In this talk, I will discuss a modification of this approach in which an unbounded potential energy is added to the total energy. Then I will discuss the behavior and singularities of the limiting maps in cases of special significance to topology. I will only assume knowledge of multivariable calculus for this talk.

**Thursday, September 22, 2016 at 3:30 p.m. in Lytle Hall 228**

**"The Research Experience: Selected Topics in Graph Theory"**

**Mr. Nathaniel Benjamin '17, Math and Secondary Education Math Major, Kutztown University of Pennsylvania **

This talk will initially address Research Experiences for Undergraduates (REUs) in a general sense by providing anecdotal descriptions and explanations, elaborating on some semantics and the benefits of such. The primary focus of the talk, however, will be on a component of the product of the Summer 2016 OEIS REU hosted by Muhlenberg College.

Graph Theory, being one of but seven projects that constituted the summer research experience, was a major topic investigated by numerous participants of the program. A large portion of the results of this research will be presented in the talk, specifically on the work completed regarding edge-distinguishing chromatic numbers and the Catalan triangle. The former topic refers to an unusual method of vertex coloring on a given graph to ensure distinct edge colors defined as an unordered pair of colors. The latter topic investigates the presence of unique, or rather non-unique, integers on an interesting number triangle constructed fundamentally from the Catalan numbers.

**2015-2016**

**2015-2016**

**Thursday, April 14, 2016 at 4:00 p.m. in Boehm Hall 260**

## Ninth Annual Thomas Pirnot Lecture in Mathematics

*"The Joy of SET®: The Mathematics In a Card Game"*

**Dr. Elizabeth McMahon and Dr. Gary Gordon, Lafayette College**

The card game SET® is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game. We’ll look at questions in combinatorics, probability, linear algebra, and especially geometry. The deck is an excellent model for a 4-dimensional finite affine geometry. If you’d like some practice before the talk, go to www.setgame.com for the rules and a Daily Puzzle.

**Tuesday, March 29, 2016 at 3:00 p.m. in Lytle Hall 218**

**"Soliton Solutions of the Nonlinear Schrödinger Equation"**

**Dr. Michelle Savescu, Department of Mathematics, Kutztown University of Pennsylvania **

The presentation starts with a brief history of solitons followed by an introduction to optical solitons and related concepts. The dynamics of the propagation of solitons through optical fibers is governed by the Nonlinear Schrödinger Equation (NLSE).

Several methods have been applied to the NLSE in order to obtain analytical soliton solutions. The methods that will be presented here are the traveling wave hypothesis, the ansatz method, the semi-inverse variational principle, the tanh method, the G′/G expansion method and the Adomian decomposition method.

Research results using some of these methods will be presented for physical models such as nano optical fibers and birefringent fibers. Bright, dark and singular soliton solutions were obtained for nonlinearity laws such as the Kerr law, the parabolic law and the polynomial law of nonlinearity.

**Thursday, March 24, 2016 at 11:00 a.m. in Boehm Hall 260**

**"Who's Who in the Politics of Math Education"**

**Dr. Mark Wolfmeyer, Department of Secondary Education, Kutztown University of Pennsylvania **

The effort to standardize a US national mathematics curriculum culminated in 2010 when over 40 states adopted the Common Core State Standards for Mathematics. How did this come to be? Who was involved and what did they set as the primary issues in mathematics education? This talk aims to provide a landscape of mathematics education policy in the United States and draws on Dr. Wolfmeyer's research contained in *Math Education for America?* (Routledge, 2014).

In an interactive presentation he will offer examples of the people and organizations involved in mathematics policy, shedding insight into the debates that exist and priorities now established. Come, mathematicians and educators, and find out where you stand on today's most pertinent issues in K-12 mathematics teaching and learning!

**Tuesday, March 22, 2016 at 3:00 p.m. in Lytle Hall 228**

**"An Evaluation of the Functional Assessment Questionnaire Using a Graded Response Model"**

**Dr. Tuan Nguyen, University of Southern California**

Alzheimer's disease (AD) is widely believed to progress over many years before any clinical symptom appears; hence, an effective treatment should be started as early as possible, especially in the preclinical stage of AD. One of the challenges to achieve this end is to find endpoints that have good sensitivity to the longitudinal decline of global functional performance.

The currently available measurements are typically obtained by assessing the patient performance on a Likert scale and summing up the resulting sub-scores to yield overall performance. An alternative approach, explored in this work, is to compute the measurement under item response theory (IRT).

Using data on the Functional Assessment Questionnaire from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, we found that IRT-based scoring increased the sensitivity to change in functional ability and improved the statistical power in future clinical trials.

**Monday, February 29, 2016 at 3:00 p.m. in Lytle Hall 214**

**"An Analysis of Non-local Elements in Differential Equations and Fractional Calculus"**

**Dr. Christopher Goodrich, Creighton Preparatory School **

In this talk we will discuss the effect of non-local elements in the discrete and continuous calculus. More specifically, we will investigate two different manifestations of non-local elements:

- the analysis of boundary value problems with nonlocal boundary conditions; and
- the nonlocal structure of the discrete fractional difference.

Finally, since we will begin by discussing the fundamentals of both the difference calculus and boundary value problems, no previous knowledge of each is assumed. A working knowledge of single-variable calculus and ordinary differential equations should be sufficient to understand a majority of the talk.

**Tuesday, February 23, 2016 at 3:00 p.m. in Lytle Hall 228**

**"A Snapshot of Complex Dynamics"**

**Dr. Sara W. Lapan, Northwestern University **

Complex dynamics is a fascinating area of mathematics that lies at the intersection of complex analysis and dynamical systems. In pop-culture, complex dynamics is known for its beautiful fractals, like the Mandelbrot set and Julia sets. This talk will be a gentle introduction to complex dynamics and, along the way, we will see and explore many beautiful fractals.

More specifically, we will focus on polynomials P(z) in one complex variable that fix 0. Every time we apply P, 0 remains fixed, but what happens to points near 0? For instance, if z is close to 0, is P(P(z)) close to 0? In complex dynamics, this type of question is of great interest.

We will discuss some of the interesting things that can happen in one complex variable. This talk will build up to the famous Leau-Fatou Flower Theorem, which provides a beautiful description of the movement of points near the fixed point for a special type of polynomial. This theorem from the early 1900s serves as inspiration for research in higher dimensions.

**Monday, February 15, 2016 at 11:00 a.m. in Lytle Hall 228**

**"Applications of Persistent Homology"**

**Ms. Leyda Almodovar, University of Iowa**

Topological Data Analysis (TDA) is a relatively new area within data analysis that combines different disciplines, such as computational topology, statistics and geometry. Many different fields have benefited from this new way of visualizing and analyzing data, such as neuroscience, linguistics and chemistry, and it is especially helpful when applied to network data.

Networks, a set of vertices representing real-world objects and a set of edges denoting relations between vertices, are very useful to model certain relations between groups of objects. In particular, I am interested in the case where these objects are brain regions, and their relations are given by anatomical connections. While the theory points to a lack of connections in certain brain regions in schizophrenic patients, neuroscientists have not been able to identify these regions using standard network theory tools.

I will present the application of persistent homology, the cornerstone of TDA, to different data sets including linguistic data, evasion paths in mobile sensor networks, and brain networks, which will be emphasized.

**Thursday, February 11, 2016 at 3:00 p.m. in Lytle Hall 228**

**"The Optimal Harvesting Policy for the Beverton-Holt Population Model"**

**Dr. Sabrina H. Streipert, Missouri University of Science and Technology**

In this presentation, the exploitation of a single population modeled by the Beverton-Holt difference equation with periodic coefficients is established. The investigation begins with the harvesting of a single autonomous population with logistic growth and it is shown that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, the optimal harvesting policy that maximizes the annual sustainable yield is investigated in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model.

In the second part, the harvested Beverton - Holt model is presented and the unique periodic solution, which globally attracts all its solutions, is derived. The investigation continues by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton-Holt difference equation.

**Monday, November 9, 2015 at 11:00 a.m. in Lytle Hall 228**

**"Hands-on Dynamical Systems"**

**Dr. Karen Keene, North Carolina State University**

In her talk, Dr. Keene will offer a hands on way for students to be introduced to the notion of solutions for dynamical systems. Participants in the colloquium will use pipe cleaners to construct an understanding of what a solution to a dynamical system looks like. Then specialized technology will move students into a more formal understanding.

Come prepared to listen, talk and work in a fun area of mathematics.

**Tuesday, November 3, 2015 at 4:00 p.m. in Lytle Hall 228**

**"Classical and Generalized Iteration"**

**Dr. Jesse Feller, Kutztown University**

The study of holomorphic dynamical systems (discrete time) is a relatively new area of study involving the repeated composition of a single function f(z) in a process called iteration. Thus we are studying the convergence of the sequence of functions f^{n}(z) = (f ◦ f ◦ ... ◦ f)(z) (n times). We will discover the concept of periodic points and classify them into the three categories of attracting, repelling or neutral. Most of our examples have dynamical properties that are easily understood. Other examples have dynamical properties that are called chaotic due to their unpredictability. We will take a look at several computer generated images of the important Julia and filled Julia sets for several examples.

Some mathematicians studying dynamics focus on composing a different function at each step of the iteration process where the function is chosen from a family according to some probability distribution. This is called random iteration. We will learn about a few recent results in this area regarding the probability that a random iteration ends up “close” to an attracting periodic point.

**Wednesday, October 14, 2015 at 4:00 p.m. in Lytle Hall 228**

**"Factor Pair Latin Squares: Be There or Be Square"**

**Dr. James Hammer, Cedar Crest College**

Sudoku has risen in popularity over the past few years. The rules are simple, yet the solutions are often less than trivial. Mathematically, these puzzles are interesting in their own right. This talk will use the idea of a Sudoku puzzle to define a new kind of n x n array. Further, we will aim to prove some necessary (and on occasion sufficient) conditions for the existence of these arrays. To that end, we define a Latin square of order n as an n x n array where every row and every column contain every symbol 1,2,...,n exactly once. We say (a,b) is an ordered factor pair of the integer n if n = a x b. An (a,b)-Sudoku Latin square is a Latin square where in addition to each row and column containing every symbol exactly once, each a x b rectangle also contains every symbol exactly once when the n x n array is tiled with a x b rectangles in the natural way. A factor pair Latin square of order n (denoted FPLS(n)) is an (a,b)-Sudoku Latin square for every factor pair (a,b) of n. This talk will mainly be concerned with the existence of such designs as well as related problems to such designs.

**Tuesday, September 15, 2015 at 4:00 p.m. in Boehm Hall 261**

**"Unsolved! History's Greatest Ciphers"**

**Dr. Craig Bauer, York College **

**Thursday, September 10, 2015 at 4:00 p.m. in Lytle Hall 228**

**"Numerical ranges: from matrices to pretty pictures"**

**Dr. Patrick Rault, State University of New York at Geneseo **

**2014-2015**

**2014-2015**

**Friday, April 10, 2015 at 6:15 p.m. in Boehm Hall 145**

## Eighth Annual Thomas Pirnot Lecture in Mathematics

*"My Favorite Integer Sequences, or, Confessions of a Sequence Addict"*

**Neil J.A. Sloane, Ph.D., Founder of the On-Line Encyclopedia of Integer Sequences (OEIS) and President of the OEIS Foundation**

**Thursday, January 29, 2015 at 3:00 p.m. in Lytle Hall 218**

**"Learning Communities: Theory, Models, Applications, etc."**

**Dr. Gil Clary, Dr. Gail Craig and Dr. Robert Ziegenfus**

**Thursday, December 4, 2014 at 3:00 p.m. in Boehm Hall 260**

*"Glitzy Math: The Mathematics of Computer Graphics"*

**Dr. Tom Pirnot, Professor Emeritus of Mathematics, Kutztown University**

**Thursday, October 2, 2014 at 3:00 p.m. in Lytle Hall 228**

*"Fun with Factoring Fantastic Forms"*

**Brian Kronenthal, Ph.D., Assistant Professor of Mathematics, Kutztown University**

**2013-2014**

**Thursday, April 17, 2014 at 3:00 p.m. in Lytle Hall 214**

**"Catalan Numbers"**

**W. H. Tony Wong, Ph.D., Assistant Professor of Mathematics, Kutztown University**

## Wednesday, March 12, 2014 at 5:00 p.m. in Boehm Hall 260

## Seventh Annual Thomas Pirnot Lecture in Mathematics

*"Pondering Packing Puzzles: Research in Recreational Mathematics"*

**Derek Smith, Ph.D., Associate Professor of Mathematics, Lafayette College**

**Thursday, November 21, 2013 at 11:00 a.m. in Lytle Hall 228**

**Thursday, November 21, 2013 at 11:00 a.m. in Lytle Hall 228**

*"Those Summer Math Nights"*

**Mr. Zachary Bales and Ms. Lauren Williams, Kutztown University '14**

**Thursday, October 17, 2013 at 11:00 a.m. in Lytle Hall 228**

*"Beliefs of Mathematics Majors"*

**Joshua Goodson, Ph.D., Assistant Professor of Mathematics, Kutztown University**

**2012-2013**

**2012-2013**

**Wednesday, March 26, 2013 at 3:30 p.m. in McFarland Student Union Building 250**

**Sixth Annual Thomas Pirnot Lecture in Mathematics**

*" Cantor and the Paradise He Gave Us"*

**Robert Vallin, Ph.D., Professor of Mathematics, Slippery Rock University of Pennsylvania**

**Thursday, February 28, 2013 at 3:00 p.m. in Lytle Hall 214**

*"Hopf Algebra Structure of Generalized Scissors Congruence Groups" *

**Jianqiang Zhao, Associate Professor of Mathematics, Eckerd College**

**Tuesday, February 19, 2013 at 3:00 p.m. in Lytle Hall 214**

*"Individual Based and Dynamic Energy Budget Models" *

**Baldvin Einarsson, University of California at Santa Barbara**

**Friday, February 15, 2013 at 3:00 p.m. in Lytle Hall 214**

*"Decomposing Graphs into Stars and Hyperstars " *

**D.P. Roberts, Assistant Professor of Mathematics, Illinois Wesleyan University**

**Tuesday, February 12, 2013 at 3:00 p.m. in Lytle Hall 214**

*"The Hopf Algebra of Sashes " *

**S.E. Law, North Carolina State University**

**Tuesday, February 5, 2013 at 3:00 p.m. in Lytle Hall 214**

*"Spying on Cages, Generalized Quadrangles and Moore!"*

**B.G. Kronenthal, University of Delaware**

**Thursday, November 1 2012 at 11:00 a.m. in Lytle Hall 228**

*" Blood, Sweat and Tears: the Cable-Trench Problem and some Applications"*

**Dr. Eric Landquist, Assistant Professor of Mathematics, Kutztown University of Pennsylvania**

**Thursday, October 18, 2012 at 3:30 p.m. in Lytle Hall 228**

*" Braids, Permutations and Games"*

**Dr. Jennifer Franko Vasquez, Assistant Professor of Mathematics, University of Scranton**

# 2011-2012

**Tuesday, March 27, 2012 at 5:00 p.m. in Boehm Hall 261**

**Fifth Annual Thomas Pirnot Lecture in Mathematics**

*" Adventures with The Moore Method as a Student and Teacher," a MILK Lecture*

**Dr. E. Lee May, Distinguished Professor of Mathematics, Salisbury University**

**Thursday, March 8, 2012 at 11:00 a.m. in Lytle Hall 228**

*" On the Collatz Conjecture," a MILK Lecture*

**Mr. Patrick Wiltrout, Kutztown University '11**

**Thursday, March 1, 2012 at 11:00 a.m. in Lytle Hall 228**

*" On Cardinality of Sets: What does `Big' or `Small' Really Mean?," a MILK Lecture*

**Mr. John Paul Jablonski, Kutztown University '13**

**Thursday, February 23, 2012 at 11:00 a.m. in Lytle Hall 228**

*" Research Experience for Undergraduates- Research Report," a MILK Lecture*

**Mr. Clinton Watton, Kutztown University '13**

**Thursday, February 16, 2012 at 11:00 a.m. in Lytle Hall 228**

*" From Finite Geometries to Translation Planes" *

**Dr. Craig Culbert, Assistant Professor of Mathematics, Kutztown University of Pennsylvania**

**Thursday, November 17, 2011 at 11:00 a.m. in Lytle Hall 228**

*" Aspects of Some Interesting Sets: A Primer" *

**Dr. Padraig McLoughlin, Associate Professor of Mathematics, Kutztown University of Pennsylvania**

**Tuesday, November 8, 2011 at 5:00 p.m. in Boehm Hall 260**

*" Thoughts on a Modified Moore Method Course in Undergraduate Analysis," a MILK Lecture *

**Dr. Alex Meadows, Assistant Professor of Mathematics, St. Mary's College of Maryland **

**Tuesday, November 8, 2011 at 11:00 a.m. in Lytle Hall 228**

*" Chomp, Chomp, Bechewy Chomp: Math and Games *

**Dr. Alex Meadows, Assistant Professor of Mathematics, St. Mary's College of Maryland **

**Thursday, October 20, 2011 at 11:00 a.m. in Lytle Hall 228**

*" Research Experience for Undergraduates- Research Report," a MILK Lecture *

**Ms. Ashley Dougherty, Kutztown University of Pennsylvania '12**

**Thursday, October 6, 2011 at 11:00 a.m. in Lytle Hall 228**

*" Using Math to Make Games fun" *

**Dr. Ryan Gantner, Assistant Professor of Mathematics, St. John Fisher College**

* *

Archives of previous colloquia are available here.

Mathematics Inquiry Learning at Kutztown (MILK) Lectures are funded by the generous support of the Academy for Inquiry-Based Learning, The Educational Advancement Foundation, and Mr. Harry Lucas, Jr.