WIMIN Talk


Plenary talks:


  • Ruth Charney, Brandeis University
     The Geometry of Groups
     This talk will be an introduction to the field of geometric group theory. In geometric group theory, we think of groups as symmetries of geometric objects. We will talk about how to construct such objects and about their strange, but beautiful geometry. The talk will conclude with an application of these ideas to robotics.

  • Jo Ellis-Monaghan, St. Michael's College
     The Phenomenally Popular Potts model, or,
    A Graph Theorist Does Physics.
     What do beer foam, ghetto formation, and tumor migration have in common? They are all complex systems where microscale nearest neighbor interactions (neighboring bubbles, neighboring residences, neighboring cells) determine macroscale properties. These macroscale phenomena can lead to bottling problems, segregation, or malignancy. How then do we model, and thereby predict, the behaviors of such systems?

    Statistical mechanics provides one tool in the q-state Potts model. Its nascent form, the Ising model, allows only two spins (up or down), and provides a model for magnetism. The Potts model with q > 2 allows more spins (thousands in the case of foam models). These models play important roles in the theory of phase transitions and critical phenomena in physics, and now have applications in every science.

    So, why would a graph theorist be interested in all this physics? The Potts model is typically constructed on various lattices. When these lattices are viewed as graphs (i.e. networks of nodes and edges), then, remarkably, the Potts model is also equivalent to one of the most renown graph invariants, the Tutte polynomial. Thus, there has been a remarkable synergy between the two fields in recent years. We will explore the Potts model, how it captures macroscale properties, its applications, and its relation to the Tutte polynomial.

Short talks:


  • Amanda Cangelosi, Smith College with Dr. Mevin B. Hooten, Utah State University

    Models for Continuous Dynamical Processes with Bounded Support
    Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty in the presence of observations. This study offers an alternative to common ecological modeling practices by using a bias-corrected truncated normal distribution to model the observations and latent process, both having bounded support. Parameters of an underlying continuous process are characterized in a Bayesian hierarchical context, utilizing a fourth-order Runge-Kutta approximation.
  • Clarice Ferolito, College of the Holy Cross
    An analogue of the Littlewood conjecture
    for formal power series with real coefficients
    The classical Littlewood conjecture roughly states that two irrational numbers can be simultaneously approximated by rational numbers with the same denominator. We follow work of Davenport and Lewis to show that the analog of the conjecture for the case of formal power series with real coefficients fails to hold.
  • Emily Gunawan, Smith College
     with Anna Boatwright, University of Georgia
    and Jennifer Koonz, University of Massachusetts
    Involutions and Conjugacy in Coxeter Groups
    A Coxeter group is a group which is generated by involutions. They are often used to study geometrical symmetries. Two finite Coxeter groups were studied, those of type Bn and those of type Dn. The research group, led by Professor Ruth Haas, was primarily interested in the conjugacy classes of the involutions of each group and the relationships between these conjugacy classes. The elements of each involution conjugacy class of Bn and Dn were explicitly determined. Formulae were found to count the order of each involution conjugacy class of Bn and to count the number of involution conjugacy classes in Bn. A relationship between the involution conjugacy classes in Bn was determined. The involution conjugacy classes in the subgroup Dn were studied.
  • Becky Hall, Wesleyan University
    The Group of Points on an Elliptic Curve
    We will examine the group of points on a non-singular cubic curve.
  • Laura Hall-Seelig, University of Massachusetts
     Comparing Two Invariants of a Curve
     Every curve has many invariants. Two of these invariants are the genus of the curve and the number of rational points on the curve. The Ihara function describes an asymptotic relationship between these two invariants for curves which are defined over finite fields. The exact behavior of this function is not known. However, many bounds for its values have been computed. Using the computer algebra system MAGMA, we have been able to improve some known explicit lower bounds.
  • Natalia Kopyra, Wellesley College
    Please Choose Me Last: The Josephus Problem
    Imagine yourself standing in a circle with 40 others in which every second person in succession remaining is to be killed except for the last one standing. Where would you place yourself so as to survive?
  • Meg Lippincott, Vassar College
    with Michael Abrahams, Vassar College
    Geometric Methods in Voting and Agreement
    Our study focused on a mathematical representation of approval voting, a voting system in which an individual’s vote consists of the outcomes they would consider acceptable. In our research, we focused on the case in which the political spectrum is Euclidean space in d dimensions, and each vote is a d-dimensional box, that is, a parallelepiped with sides parallel to the coordinate axes. Two or more votes are said to agree if there is a platform (a point in the spectrum) that is shared by all of them. We call a society (2,3)-agreeable if, given any three voters, at least two of them agree on a common platform. Our goal was to study the agreement proportion of such societies, or the maximum percentage of a society that could be satisfied by a single platform. In dimension 1, the agreement proportion is 50%, and this bound is sharp. We know that the agreement proportion in dimension 2 is no more than 3/8, or .375. Our main result is that a (2,3)-agreeable society in any dimension must have a positive agreement proportion – in particular, in dimension 2 the agreement proportion must be at least 0.2324…
  • Emily Marshall, Dartmouth College
    with Geoff Patterson, Grand Valley State University
    Gerrrymandering and Shape Compactness
    The American Heritage Dictionary defines gerrymandering as the act of “dividing a geographic area into voting districts so as to give unfair advantage to one party". The problem of gerrymandering has led to the development of several mathematical measures of shape compactness, some of which have been used in court cases to argue for or against the legality of congressional redistricting plans. In this talk, we will show how the notion of convexity can be used to detect irregularly shaped districts. We will explore both theoretical and empirical aspects of this convexity-based measure of shape compactness.
  • Alison McDonough, Smith College
    with Rebecca Tramel and Priscah Cheruiyot, Smith College
    DeBruijn Sequences and Linear Recurrences
    DeBruijn sequences are an interesting class of combinatorial objects. We will define what a DeBruijn sequence is and give examples. We will then describe the connections between DeBruijn sequences and sequences defined by linear recurrences.
  • Cordelia McGehee, Smith College
    with Gillian Riggs, Smith College and
    Samantha Oestreicher, University of Minnesota
    Configuration Spaces in Phyllotaxis
    Phyllotaxis is the study of plant organ arrangements such as the scales on a pine cone or the florets on a sunflower. A simple model for these arrangements consists of stacking disks on the surface of a cylinder. The resulting configuration is determined by the initial chain of disks around the cylinder. In this talk, we will examine some of the configuration spaces of those chains.
  • Bailey Meeker, William Smith College
    with Jonathan Forde, Hobart and William Smith Colleges
    A Model of Varicella Zoster Virus Reactivation
    We created a model of the initial infection and reemergence of Varicella Zoster Virus, which causes the Chicken Pox and Shingles. We explore this model's behavior and discuss the timing of the new Zoster vaccine to prevent the elderly from getting Shingles.
  • Sylvia Naples, Bard College
    The search for an upper bound on the number of graceful
     labelings of a path with $n$ edges
    The concern of this talk is to provide an effective way to measure the rate of growth for the number of graceful labelings of a path graph with $n$ edges, as $n$ increases. We introduce the \textit{graceful labeling diagram}, which we use to systematically construct graceful labelings, and develop analytical tools that exploit the structure of the diagram to compute an upper bound on the number of graceful labelings of a path. We conjecture that a path with $n$ edges has order of $\log(n) \log (n-1)\ldots \log (2)$ graceful labelings.
  • Jasmine Nirody, Boston University
    with Raphiel Murden, Washington University in St. Louis
    David Pinney, Cornell University
    and Miklos Racz, Budapest University of Technology and Economics
    Modeling and Measuring Unstable Behavior in Hematopoiesis
    A modification of the age-structured model of hematopoiesis as presented in B´elair, et. al., (1995), is proposed to study the negative feedback loop between erythropoietin and hemoglobin. The system of equations is reduced using the method of characteristics to a pair of threshold-type delay differential equations and then linearized locally around the equilibrium point for stability analysis. We attempt to show the existence of Hopf bifurcations in physiologically reasonable parameter space. A numerical approximation of the unreduced model is provided as an efficient and useful tool to investigate the parameter space. Simulations using this model provide strong evidence of a bifurcation in biologically significant parameters.
  • Weiwei Pan, Wesleyan University
    Categorification of Topological Invariants
    A principal concern of topology is the differentiation of non-homeomorphic spaces. One method of accomplishing this goal is to capture parts of the topological information of spaces with algebraic objects. We will review the geometric construction of some standard algebraic invariants of spaces (such as homotopy, ordinary homology and K-theory groups), and discuss how the categorification of these constructions yields yet more sophisticated invariants.
  • So Eun Park, Columbia University
    The group of symmetries of the Tower of Hanoi graph
    I prove that the group of symmetries of the Tower of Hanoi graph with k pegs and n disks, denoted H_n^k, is isomorphic to the group of permutations of k elements, S_k, for all k greater than or equal to 3 and positive n.
  • Emma Schlatter, Smith College
    with Jim Henle, Smith College
    Nimrod: A New Take-Away Game
    Nimrod is similar to a class of combinatorial games known as take-away games. In take-away games, two players take turns removing a given number of counters from a pile or piles, and the first player unable to move loses the game. But Nimrod has a twist: the number of counters a player can remove depends on the number her opponent removed last turn. The result is a complicated and mysterious game. I'll share some of the things we've discovered about Nimrod, and questions still open.
  • Kristin Tyler, Smith College
    with Barbara Calvert, Elan McCollum, and Siobhan O'Riordan, Smith College
    Drinking games, conditional probability and calculus
    Drinking games (DG) facilitate heavy alcohol consumption in a short period and are associated with negative experiences. We examined the utility of the Alcohol Use Disorders Identification Test (AUDIT) cut-off scores to identify DG involvement in a sample of female college students. We used Receiver Operating Characteristics (ROC) curve analysis, which plots the true positive rate (Sensitivity) against the false positive rate (Specificity) to graphically determine the optimal cut-off point for an AUDIT score. Findings indicated an AUDIT score of at least 5 is needed to identify gamers among students at a women's college.
  • Amy Wesolowski, Smith College
    Network Analysis of the Clique Replacement Graph
    A polytope is defined to be a convex hull of a finite set of points. Clique replacement is a technique to produce a new poltyope from an existing one. We can create a graph whose vertices are polytopes and whose edges are clique replacements. This talk describes the application of the mathematical tools of emerging complex networks to the clique replacement graph. Statistical methods for quantifying relationships and clusters between elements of the clique replacement graph are used.
  • Sarah Wright, Dartmouth College
    Graphs Three Ways
    This talk will cover the basics of three different concepts of a graph. We'll discuss how each of these ideas lead to results in the area of C*-algebras and a possible next step in this research area.



Last update: 7/23/08