Department of Mathematics Colloquium

                                                     SPRING 2014


                                                                    Model Theory for Metric Spaces:

                                                                       Ultraproducts and Stability

                                                                            Dr. Alexander Berenstein

                                                                                    Universidad de los Andes
                                                                                           Bogota, Colombia
                                                                                                 12:20 -1:20 p.m.

                                                                                                Thursday, January 9, 2014

                                                                                                                Luter 372


                                                                                Independence and Linearity:

                                                      Model Theoretic Perspectives


                                                                       Dr. Yevgeniy Vasilyev

                                                         Memorial University of Newfoundland 

                                                                                           12:20 -1:20 p.m.

                                                                                 Thursday, January 23rd, 2014

                                                                                                 Luter 372

Abstract: Linear independence and algebraic independence are fundamental concepts used to describe linear or polynomial relationships between mathematical objects. Model theory, a branch of mathematical logic studying mathematical structures from the point of view of a formal language, provides a framework in which linear independence and algebraic independence are viewed as special cases of a more general notion.  Using this approach, we can define  analogues of the basic concepts of linear algebra, such as span, basis and dimension, in an arbitrary mathematical structure satisfying certain “geometric” requirements.

In this talk, I will define the notions of “geometric structure” and “pregeometry”, and discuss the question of distinguishing between  linear (“vector space-like”) and  non-linear geometric structures.


Riemann Zeta Function at Integers

Hongwei Chen, Ph.D.

Christopher Newport University

12:20 - 1:20 PM

Thursday, February 6, 2014

Luter 372

Abstract: Riemann zeta function is one of the most important and fascinating functions in mathematics.  This talk is in two parts: the first part is about the history and significance of the Riemann zeta function, including the Riemann hypothesis; the second part is about my recent work on the values of the subseries of the Riemann zeta function at integers. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.


An Introduction to Saturation Problems in Graph Theory

Dr. Paul Wrayno

Christopher Newport University

12:20 - 1:20 PM

Thursday, February 20

Luter 372

Abstract: Broadly speaking, saturation problems are concerned with finding and analyzing graphs that "almost" have a particular desired or forbidden property. The most well studied saturation problems are extremal problems where one asks "How large/full can a graph be while avoiding this property?" Another type of saturation question asks "How small/sparse can a graph be while still being saturated?" A third type of saturation question asks "For what sizes is there a saturated graph?" The first two question types give upper and lower bounds for these sizes, but it is interesting to know whether there is a saturated graph of each size between the upper and lower bounds, and whether and where gaps occur in that interval.

More formally, a graph G is F-saturated if G does not contain a copy of F, but with the addition of any new edge it does. A graph is an extremal graph if it is an F-Saturated graph of maximum size and its size is the extremal number. The saturation number in contrast is the minimum size of any F-saturated graph.

This talk will provide an introduction to basic properties of mathematical graphs, extremal and saturation numbers and present a sampling of saturation results. If time allows, Dr. Wrayno will discuss his own work on a saturation problem.


Competition and Community Composition

in streams and rivers

Dr. Olga Vasilyeva

 Department of Mathematics

  Christopher Newport University  

12:20 - 1:20 PM

Tuesday, March 18, 2014

Luter Hall 372

Abstract: The flow speed in stream and rivers can change due to natural causes or human activities. Any change in flow speed can impact biological communities in streams and rivers that are shaped not only by their biotic interactions but also by their response to water flow. In this talk, we will discuss some transport-based modelling approaches describing the population dynamics of two or more competing species in stream ecosystems. We show that alterations of flow speed can influence the outcome of competition and thereby change community composition. Our analysis shows that at relatively high flow speed, each species' intrinsic growth rate is the crucial factor that determines the outcome of competition. At low flow speeds, in contrast, the strength of interspecific competition determines community composition. This is a joint work with Frithjof Lutscher, University of Ottawa, Canada.


Two predator-prey models

with a Holling-type I functional response that has a

sharp corner in its graph

Dr. Gunog Seo

Department of Mathematics

Colgate University

12:20 - 1:20 PM
Thursday, March 20, 2014
Luter Hall 272
Abstract: Mathematical biology is one of the fastest growing interdisciplinary areas in applied mathematics. In particular, the subject of mathematical ecology is one of the oldest in mathematical biology and recently grabs a lot of attention of mathematicians and biologists. Among many themes in mathematical ecology, the study of the dynamics of predator-prey interaction is a popular subject. In my talk, I will present the dynamics of a laissez-faire and a Leslie predator-prey model with a Holling type I functional response, which is a monotonically increasing function that tends toward and reaches a maximum per capita consumption rate as the prey density increases. I study local and global stability of the equilibrium where the predator and prey coexist. For the Leslie-type model, I use a generalized Jacobian of Clarke to determine how eigenvalues jump at the corner of the functional response.  In my numerical results, I show that both models can possess two limit cycles that surround a stable coexistence equilibrium and that the cycles arise through a global cyclic-fold bifurcation. To smooth out the sharp corner of the type I functional response, I introduce an arctangent approximation. I analyze the same models with an arctan functional response and show both models possess Hopf, cyclic-fold, and Bautin bifurcations.


Numerical Evidence of Reverse Buoyancy Current

in a Channel


Dr. James Martin

Christopher Newport University

12:20 - 1:20 PM

Thursday, April 3, 2014

Luter 372

Abstract: This talk will focus on my numerical calculations of gravity-driven channel flow.  Upstream particle seeding is used as one trigger for the starting density gradient in the two included fluids. During the ash fall-out period of volcanic eruption, a spectacular instance of a particle-driven current takes place with the super-heated neighboring air. A more everyday gravity-driven current takes place upon opening your front door and letting the air enter/exit on a cold day. Under certain initial conditions, a time sequence of density contours reveals evidence of the phenomenon known as reverse buoyancy. I will begin this talk, however, with old photographs from Main Steet Library's Virginiana room and other reasons for my ongoing interest in the subject of aerodynamics and fluid flows.

Department of Mathematics Colloquium

Fall 2013

September 26, 12:15 - 1:15, Luter 372

Dr. Emily Sprague

Edinboro University

A mathematical discussion of what makes

 good music sound “good”


Abstract: Throughout history, mathematicians have argued whether mathematics drives or describes music.  During the twentieth century the pendulum swung in favor of the “intellect over the ear” as musicians famously developed serial composition, then turned to probability theory to eliminate any hint of traditional melodic and harmonic structure.  Music theorist Allen Forte, in his book The Structure of Atonal Music, proposed a musical "set theory" of pitch-class-set analysis analogous to mathematical set theory in an attempt to provide a method for the analysis of this atonal music.

By the final decades of the last century, music theorist John Clough became interested in extending Forte's atonal methodology to the diatonic system, the scale and interval patterns of our familiar tonal music. Among other goals, he hoped to advance discussion of how to classify with mathematics, music that is pleasing and interesting to the general ear.

This presentation will survey the building blocks, developed by Clough together with mathematician Jack Douthett, of some descriptive set theory which points toward characterizations of scales and intervals of tonal systems.  Following this survey, we will review work of Godfried Toussaint who has applied similar techniques to analysis of musical rhythm.  In particular, we will illustrate an isomorphism of scale and rhythm and move on to his exploration of the qualities that make a particular rhythm "good."

October 10, 12:15 - 1:15, Luter 372

Dr. Yevgeniy Vasilyev

Christopher Newport University

Model Theory: the geography of mathematics

October 24, 12:15 - 1:15, Luter 372

Dr. Paul Wrayno

Christopher Newport University

Extremal and Saturation Graph Theory

November 7, 12:20 - 1:20, Luter 372

Dr. Olga Vasilyeva

Christopher Newport University

Against the flow: population dynamics of stream insects and drift paradox

November 21, 12:15 - 1:15, Luter 372


Biomathematics Semester


Christopher Newport University


Department of Mathematics Colloquium


Spring 2013 Schedule



  • February 14, 12:15 – 1:15, GOSN 202           MODELING THE INFLAMMATORY RESPONSE

Dr. Angela Reynolds
Virginia Commonwealth University



  • February 28, 12:15 – 1:15, GOSN 202


    Dr. Natalia Toporikova

    Washington and Lee University



    • March 21, 12:15 – 1:15, GOSN 202


                                                                        OF CARDIOVASCULAR DISEASE

      Dr. Laura Ellwein
      Virginia Commonwealth University



      • March 28, 12:15 – 1:15, GOSN 202 

                                                                PATTERN FORMATION AND CHAOS IN BIOLOGY

        Dr. Heather Hardway

        Christopher Newport University



        • April 11, 12:15 – 1:15, GOSN 202

        Dr. Jing He

        Old Dominion University

Dr. Heather Hardway

Christopher Newport University

Thursday, September 20, 2012   Gosnold 202

12:20 - 1:20 PM

Reaction-Diffusion Models for Dorsal-Ventral Patterning in Development

Dr. Ken Hicks 

Ohio University

Feb. 8, 2012        Wednesday, 3 p.m.  Gosnold 202

Dr. Heather Hoffman

George Washington University

March 14, 2012      Wednesday, 3 p.m.  Gosnold 202

Among the Creationists
Dr. Jason Rosenhouse
Nov. 15, 4-5 p.m.
Forbes 1022

In 1999, the Kansas State Board of Education voted to remove the theory of Darwinian evolution from its state science standards. In 2000, I accepted a post-doctoral position in mathematics at Kansas State University. The juxtaposition of these two events led to my persistent interest in evolution and creationism. For the past decade I have indulged that interest by becoming a regular attendee at creationist conferences and other gatherings. This experience has provided me with a better understanding of why evolution continues to provoke so much opposition. In this talk I shall relate a number of anecdotes that are typical of my experiences among the creationists, explain the major aspects of creationist thought and argumentation, and discuss how these issues relate more broadly to questions about the relationship between science and religion.

The Monty Hall Problem, Reconsidered
Dr. Jason Rosenhouse
Nov. 16, 3-4 p.m.
The Freeman Center, 202

Imagine that you are a game show contestant. You are shown three doors, and told that one of them conceals a car. The other two conceal goats. You choose one of the three doors, but do not open it. The host of the show now opens one of the other two doors, careful always to open one that conceals a goat. He now gives you the option of either sticking with your door, or of switching to the other unopened door. Which option should you choose to maximize your chances of winning the car? This is the Monty Hall problem, and it fools just about everyone. The intuitively obvious answer, that it makes no difference whether you stick or switch, turns out to be incorrect. There is actually a big advantage to be gained from switching doors when permitted to do so. We shall explore the history of the problem and explain why the obvious answer is incorrect. We shall then show how variations on the problem can be used to promote clear thinking about probability.

Nov. 30, 3  p.m.
Gosnold 202