Spring 2020
April
4/23
Dr. Laura Taalman, James Madison University
Coding and Generative Design for 3D Printing
3D printing and design allows us to physically experience complex mathematical objects. In this talk we’ll take a 3D-printed tour of mathematical knots, tessellations, fractals, and polyhedra. Using code and generative design we can create parametric models that leverage randomness to achieve structural variety or even organic-looking behavior. We’ll also talk about iterative design, the ability to “learn by failing,” and the importance of being open to sharing that process, both in 3D design and in mathematical exploration.
4/16
Ana Wright, University of Nebraska-Lincoln
A Journey Through Hyperbolic Space
Hyperbolic geometry shows us a strange land of skinny triangles, where squares can't exist. In this talk I will introduce the ideas of hyperbolic geometry and how we can visualize it. I will also talk about how we can use this geometry as a tool to study topological objects, like knots!
4/9
Dane Miyata, University of Oregon
An Introduction to Gröbner Bases:Why Polynomial Long Division is Actually Awesome!
Until recently, we assumed that disease spread could be adequately predicted using a model that assumed an even spread of Infectious and Susceptible subjects across a population and that we only needed to consider the mean number of interactions. We were wrong. Proceeding from work done in the past 20 years, we will explore the importance of network structure in how disease will spread. There will also be memes.
4/2
Dr. Christian Hampson, Willamette University
Spreading Disease and Memes on a Network
Until recently, we assumed that disease spread could be adequately predicted using a model that assumed an even spread of Infectious and Susceptible subjects across a population and that we only needed to consider the mean number of interactions. We were wrong. Proceeding from work done in the past 20 years, we will explore the importance of network structure in how disease will spread. There will also be memes.
March
3/5
Dr. Kathrine Mclaughlin, Oregon State University
Estimating the Size of Hidden Populations using Respondent-Driven Sampling
February
2/28
Dr. Leanne Merrill, University of Oregon
The Magical Number 9
What is so magical about the number 9? Throughout history, the number 9 has fascinated people across the world and has played an important role in scientific, cultural, and spiritual thought. We examine the history, significance, and mathematical properties of 9 through the medium of magic. We will learn magic tricks involving the number 9, and examine these tricks through the lenses of both elementary and abstract algebra. Audience participation is encouraged!
January
1/30
Professor Shabnam Akhtari, University of Oregon
Quadratic Forms; From Gauss to Bhargava
One of the simplest problems in mathematics is to find all of the solutions of a given equation. If we are searching for integer solutions then this is a much deeper problem than just finding all complex solutions. A very important and classical problem in number theory is the question of which integers are represented by a given polynomial. For example, what integers are represented by x^2 + y^2, as x and y run through all the integers? We will focus on quadratic equations, those of degree two. There is a long and rich history and at the same time many unsolved problems about representation by quadratic equations. We will explain some classical and contemporary ways to study which integers are indeed represented by binary quadratic forms.
Fall 2019
November
11/21
Professor Blessing Emerenini, Oregon State University
Hallowing Effects
Majority of bacteria are known to live in communities called biofilms. Biofilm formation is characterized by the balance of attachment, growth and detachment of cells from mature biofilm, this can be externally or internally induced, leading to sloughing, erosion or seeding. Quorum Sensing is a cell-cell-communication mechanism used to coordinate gene expression and behavior in groups based on population densities. I present a mathematical model that studies the hallowing effect of quorum sensing induced cell dispersal.
11/14
Professor Yung-Pin Chen, Lewis and Clark College
Random Walks on Rectangular Lattices
I will begin with random walks on one-dimensional lattices before looking at random walks for the two-dimensional cases. I will focus on the hitting probabilities associated with symmetric random walks starting at a node in a bounded rectangular grid. In particular, I will show the work for finding the hitting probability that a symmetric random walk reaches the north or south boundary before the east or west boundary of a bounded rectangular grid.
October
10/31
Professor Heather Smalley Kitada, Willamette University
Spooky Statistics
One of the scariest parts of statistics is model misspecification (if you assume certain functional form but are incorrect). This has vast implications for any subsequent inference derived. Therefore, the goal of this research is to explore and develop methodology for new hypothesis testing to aid survey researchers in choosing modeling techniques for mode effect adjustments based on complex data applications. The proposed goodness-of-fit tests will address the construction of model residuals, creation test statistics, and reference distributions(empirical/bootstrap vs theoretical).
10/10
Professor Erika. B. Roldan Roa, The Ohio State University
The Mutando of Insanity
Instant Insanity is a puzzle that consists of four cubes with colored faces. Each face is colored with one of four possible colors and each one of these four colors should be present on each of the four cubes. In this talk, we discuss two different mathematical models of the puzzle: one that involves labeled graphs and another that involves matrices with a touch of number theory. We use the combinatorial with number theory model to generate a new family of related puzzles, to analyze their solutions, and to propose interesting generalizations about the puzzle in higher dimensions. And, of course, we find new variations of the puzzle with very interesting properties as The Mutando of Insanity.
September
9/19
Sam Johnston, Willamette University
Introducing the Mathematics of Option Trading Through Sequential Regression in Discrete Market Models
Financial trading today is a business conducted almost exclusively by computers, using algorithms designed to approximate the values of assets and maximize an investor's expected return through trading. In this talk, Sam introduces the mathematical background to option trading using discrete market models. When examining certain strategies for replicating options, it is of interest to subject the model to error and observe the effect on the hedging process. He also explores the sequential regression hedging strategy, which was the focus of his summer research at the University of Connecticut.
9/12
Sam MacDonald, Willamette University
The Complexities of Convexity
Neural codes are mathematical models of neural activity. Neuroscientists have discovered neurons called place cells which fire when animals are in specific (and usually convex) regions in space. Through monitoring these place cells and recording data on when they fire, we can construct neural codes, which tell us which neurons fire together. Of particular interest to the mathematical community is identifying which codes can be represented by open or closed convex sets, which was the subject of my summer research at Texas A&M University and will be explored in depth during this talk.