Math Mondays

Join us to hear Jacob Smith, assistant research professor of statistical science and political science at Duke University, discuss spatial regression in an elevator.

In 2005, elected North Carolina Labor Commissioner Cherie Berry had her picture installed on every inspection placard in North Carolina. Using spatial regression modeling, I found that in counties where there were more elevators, she improved on her performance in subsequent elections. While Berry retired in 2020, this research has implications for advertising and elections in other settings, as numerous other officials have their picture and/or name placed in an official capacity.

Learn more about this presentation on Monday at 3:10 p.m. in Hayes 109.

Join us to hear Visiting Assistant Professor Frankie Chan from the North Dakota State University discuss the study of triangles in euclidean, spherical and hyperbolic geometry. 

In this talk, we will discuss notions of lines, distances, angles, and distance-preserving transformations appearing in these 2-dimensional geometries. We will focus on triangles in the hyperbolic plane, which comes with really nice pictures! If time permits, we will also briefly discuss my research on triangle groups involving studying particular symmetries of triangle tessellations in the hyperbolic plane.

Learn more about this presentation on Monday at 3:10 p.m. in Hayes 109. 

Join us to listen to Axel Brandt, assistant professor of mathematics at Northern Kentucky University, discuss the use of graphing and multi-variable polynomials to help avoid everyday conflicts.

Chocolate vs. Vanilla. Cats vs Dogs. Proud Boys vs Antifa. Dems vs Republicans. Conflicts abound, but how do we determine if a conflict is avoidable? And when it is, how might we avoid it?

In this talk, we explore the mathematics of how to (at least theoretically) avoid some conflict in the U.S. House of Representatives. Specifically, we use graph coloring as a model for scheduling committee meetings. We then develop a method for creating multi-variable polynomials whose roots correspond to scheduling conflicts before using the Combinatorial Nullstellensatz to determine when we can avoid them.

Join us on Monday, March 21, from 2:10 to 4 p.m. in Hayes 109 to hear the presentation. We hope to see you then!

Join us to listen to Professor Skon, from the Department of Mathematics and Statistics at Kenyon, discuss modern wifi solutions. 

Modern Wifi solutions are inexpensive for home and small office deployments.  In contrast, "managed" WiFi solutions, the kind used for schools, hotels, corporations, retail, airports, sports arenas settings, cost from $1500-$3000 per deployed Access Point. The reason for this high cost is largely based on the software required to give the Access Points the functionality needed for managing users, connection security, bandwidth sharing, and accounting.

Professor Skon is currently involved in a project to develop free, open source software which will operate on inexpensive, widely available wireless hardware, with the goal of reducing the cost of a managed wireless network by a factor of 10. In this talk I will give some history of WiFi, and discuss the solution being developed.

Join us on Monday, Feb. 28 from 3:10 to 4 p.m. in Hayes 109 to hear the presentation. We hope to see you then!

Douglas T. Pfeffer, visiting assistant professor at Berry College, will discuss the Toeplitz matrices and their infinite-dimensional analogs. 

A Toeplitz matrix is one in which every diagonal is a constant value. Such matrices pop up frequently in signal processing and information theory. As such, traditional questions are raised regarding their inversion, eigenvalues, etc. The goal of this talk is to introduce these matrices, look at their basic properties, and then take a tour of the machinery necessary to discuss their infinite-dimensional analogue: the Toeplitz operator. This tour assumes knowledge of linear algebra, calculus 1-3, and a geometric understanding of complex numbers. Once introduced, we will look at some of their properties and revisit the same traditional questions as before.

Join us on Monday, Feb. 21, from 3:10 to 4 p.m. in Hayes Hall 109 to hear the presentation. We hope to see you then!

Edward Price, assistant professor in the Department of Mathematics and Statistics at Grinnell College, will discuss implicitization and the Rees Ring. 

Parametric equations can often be very useful for graphing shapes, such as curves and surfaces. Details about these shapes can often be difficult to determine from the parametric equations, however, so we may wish to eliminate the parameter and obtain implicit equations describing the shape. The process of converting from parametric equations to implicit equations is called implicitization. Many branches of study care about implicitization. For example, certain problems in graphical modeling, chemical reaction networks, and algebraic geometry can be reduced to implicitization problems.

When the parametric equations are polynomials or rational functions, commutative ring theory can be used to solve the implicitization problem, particularly through the use of the Rees ring. In this talk, we will introduce the implicitization problem, demonstrate how it can show up in algebraic geometry, and explain how the Rees ring can be used to solve the implicitization problem.

Join us on Monday, Feb. 14, from 3:10 to 4 p.m. in Hayes Hall 109 to hear the presentation. We hope to see you then!

Join us to listen to Nick Connolly, a postdoctoral researcher at the French National Research Institution, and Kenyon alumnus, discuss rational tangles in relation to his dissertation research.

"Tangles are knot theoretic structures that can be thought of as the building blocks of mathematical knots. They were first introduced by the mathematician J. H. Conway, who showed how small knot diagrams can be cataloged using certain configurations of tangles. My doctoral research focused on the tabulation and classification of 2-string tangle diagrams, which can be divided into different classes based on their construction. In this talk, I will provide a brief overview of the most well-understood of these classes: the rational tangles, which have a particularly elegant construction. In addition to discussing rational tangles, I will also share some highlights from my dissertation research concerning more advanced classes of tangle diagrams."

Learn more about this presentation on Monday at 3:10 p.m. via this Zoom link.

Join us to listen to Visiting Professor Subhadip Chowdhury of the College of Wooster discuss rotation number and dynamics on the circle. 

The theory of Dynamical Systems is the study of how something evolves over time. This includes population growth models, viral epidemic projections, and fancier topics like Chaos Theory and fractals. We will discuss one of the simplest and most fundamental dynamical systems: maps from the circle to itself (as a simpler version of periodic processes), and introduce a numerical invariant called "rotation number" that encodes interesting dynamical properties of such maps.

Learn more about this presentation on Monday at 3:10 p.m. via this Zoom link.

Join us to hear Assistant Professor Matt Zaremsky from the University of Albany discuss the study of group theory.

Group theory can be viewed as the study of symmetries of geometric objects, via abstract algebraic tools called "groups." Conversely, when handed an abstract group, one might hunt for a geometric object whose symmetries it describes. This talk will be an introduction to the interplay between geometry and algebra, via some of my favorite groups. Along the way I will discuss a colorful cast of characters such as: groups of permutations, groups of braids, groups of matrices, and my favorite, a class of groups with the unfortunately non-descriptive name "Thompson's groups."

Learn more about this presentation on Monday at 3:10 p.m. via this Zoom link.

Join us to hear Ph.D. student Anna Seffernick discuss the use of a Bayesian Stereotype Model for feature selection in acute myeloid leukemia. 

Ordinal outcomes are common in public health and medical research and often represent the observed cutpoints of some latent continuous variables. However, some ordinal outcomes are truly discrete and their categorization relies on the subjective combination of several factors. One example of this type of ordinal variable is the European LeukemiaNet (ELN) risk stratification system, which characterizes acute myeloid leukemia (AML) patients as having favorable, intermediate, or adverse risk. Because AML is a heterogeneous mix of diseases, accurate classification of AML patients can have important prognostic and treatment implications. Thus, we are interested in identifying genomic features that are monotonically associated with ELN score, as these might be mechanistically related to disease severity or progression and could be useful as diagnostic markers or potential therapeutic targets.

The stereotype logit model was developed for these discrete, or “assessed”, ordinal variables. Though not widely used, this model has been implemented in high-dimensional settings with the frequentist GMIFS algorithm and in the Bayesian setting with low-dimensional data. Here, we extend the Bayesian framework for the stereotype model to high-dimensional data and explore different regularization and variable selection priors. Simulation studies were conducted to investigate the feature selection performance of these priors, as well as to compare our method with existing methods. We also applied our proposed model to an AML gene expression dataset to identify genomic features that might be driving patients’ cytogenetic risk group classification. 

Learn more about this presentation on Monday at 3:10 p.m. via this Zoom link.

Join us to listen to Ph.D. scholar C.J. Argue of Carnegie Mellon University talk about the field of online algorithms and finding possible solutions to problems in online learning.

The field of online algorithms considers computational settings in which algorithms make permanent real-time decisions while receiving input over time. The challenge lies in making decisions that will be nearly optimal for a range of possible future scenarios. In this talk, I will discuss two directions within online algorithms. The first is the Convex Body Chasing problem, a geometric form of convex optimization in an online setting. I will show the resolution of a long-standing question. Secondly, I will discuss a new model of Secretary problems aimed at bridging between worst-case and average-case models, and make connections to problems in online learning.

Learn more about this presentation on Monday at 3:10 p.m. via this Zoom link.

Join us for the exciting introduction to Kenyon's brand new Sports Analytics Society which explores sports, statistics, and their mutual relationship.

With the rise of data analysis in sports and the increasing desire for teams to gain every competitive advantage they can get, the sports analytics industry is growing at a rapid rate. Join us to learn more about one of Kenyon's newest student organizations, the Sports Analytics Society! We'll discuss the history of sports analytics at Kenyon and past research that has been done, looking at data from various sports at varying levels of play, including Kenyon's own athletic teams. We'll also talk about the goals for the club and what you can expect to see from us in the future. If you like statistics, sports or both, please join us!

Come learn more about the latest student organization with our speakers on Monday at 3:10 p.m. in Hayes Hall 311 or via this Zoom link.

Join us to listen to fellow Kenyon students share their valuable experiences and talk about possible opportunities regarding internships in the math-stat and sci-comp fields.

Are you curious about what internships look like in math or related fields?Join us for a student internship panel. Hear your peers discuss their recent internships and share their experiences with you. Lori Gastin from Kenyon’s Career Development Office (CDO) will also share some details about how the CDO can support you in the process of securing an internship. 

Come learn more about these internships with our student panel on Monday at 3:10 p.m. in Hayes 311 or via this Zoom link.

Join us to listen to Professor Ellen Veomett from St. Mary's College of California talk about gerrymandering and its solutions in a mathematical context. 

Do you want to learn how to use mathematics to improve our democracy? Then join us as we discuss mathematical tools to detect and prevent gerrymandering. Gerrymandering occurs when district lines are drawn in a way to benefit a group of voters (and thus disenfranchise another group of voters). In this talk, we'll discuss how gerrymandering happens, and metrics that have previously been used in court cases claiming that gerrymandering has occurred. We'll also introduce a new metric, the Geography and Election Outcome (GEO) metric which is an improvement on prior metrics. It uses both map data and partisan data to detect the existence of gerrymandering, as opposed to just one or the other (as prior metrics do).

Come explore this fascinating intersection of math and politics with us on Thursday at 12:10 p.m. via this Zoom link.

Join Professor Erin Leatherman to discuss past experimental research done by Kenyon Summer Science Scholars and the exciting upcoming opportunities. 

Traditional experimentation involves manipulating one or more input variables of interest to explore the effect of the variable(s) on a particular response, where the manipulation is done on a physical object or system. Unfortunately, traditional experimentation is not always feasible due to financial, time, or ethical constraints. In cases where it is possible to construct a mathematical model of the object/process, implementing this mathematical model using computer code can be a feasible experimental alternative. The encoded mathematical model is called a simulator, and the simulated experiment is called a computer experiment. This talk will highlight some computer experiment projects from past Kenyon Summer Science Scholars who have worked in the Leatherman Lab and will discuss some possible projects for upcoming summers.

Join us on Monday, Oct. 11, in Hayes 311 or via this Zoom link.

Come hear Visiting Assistant Professor Adam Lizzi discuss how the most modern mathematical concepts were articulated by masters of the eighteenth century. In his own words:

"Fermat was the first to discover that prime numbers come in two different flavors: some of them, like 89, can be written as the sum of two squares [89 = 25 + 64!] while others, like 19, admit no such description. Which primes fit in which category, and why? I'll show you how Euler approached the problem in this talk, then look at other similar conjectures made by Fermat, Euler, Legendre, and Gauss. Along the way we'll see some of the ways in which the old masters attempted to articulate modern concepts that were ahead of their times. I'll try to give you a bird's-eye view of how these conjectures have been settled by the end of the talk. This seemingly innocuous question is linked to some of the most powerful algebraic and number-theoretic ideas of the eighteenth, nineteenth, and twentieth centuries!"

This combination of math and history is one you don't want to miss. You can join us at 3:10 p.m. in Hayes 109 to hear the presentation, or you can join us by clicking on this Zoom link.

Enjoy a welcome back reception to the Math and Stat department. Meet other students and members of the department and discuss what's happening this year in mathematics. Join us at the Science Quad at 3:10 p.m.

Enjoy another double presentation by Kenyon's own math and statistics students. Join us for another virtual event by clicking on this Zoom link.

Our first speaker will be Dev Akre '23 on "An Equivalence Algorithm For ConstaCyclic Codes." Recently, a new algorithm to test the equivalence of two cyclic codes has been introduced which is efficient and produced useful results. We generalize this algorithm to constacyclic codes. This algorithm is both more CPU and memory efficient than existing methods for checking equivalence computationally. As an application of the algorithm we found many cyclic and constacyclic codes with good parameters and properties. In particular, we found 23 new codes that improve the minimum distances of BKLCs.

Second, we will have Matthew J. Harrington '22 presenting on "Good Codes From Quasi-Cyclic Codes Using ConstructionX." One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is a generalization of cyclic codes known to be fertile to produce such codes. Using ConstructionX, a ternary operation on codes and some important properties of QC codes, we were able to find 35 codes with better parameters than any previously discovered code. In this talk, we will explore what ConstructionX does, and how QC codes are well suited to it for use in producing new best known linear codes.

Math and statistics is presenting a double feature of student-led presentations! Join us for another virtual event by clicking on this Zoom link.

Our first speaker will be Prashant Bhandari '22 on "Estimating Vaccine Hesitancy Based on Smoking Status among Ohio Population." Several studies have found increased risk of ICU admission, symptom, severity and mortality among the smokers. Given these findings, smokers, and people with a history of smoking should be encouraged to take COVID-19 vaccine. In this study, we want to find whether COVID-19 vaccine hesitancy based on smoking status prevailed in Ohio. We use the data from the Ohio Covid-19 Survey (OCS) and Ohio COVID-19 survey OMAS. After controlling for demographic and socio-economic characteristics, we find a significant association between smoking status and vaccine hesitancy. This project was sponsored by Kenyon OSU and Pelotonia.

Our second speaker will be Eli Hiton '23 on "Analysis of Glaucomatous Eyes Using Machine Learning." Non-invasive retinal imaging of glaucomatous eyes can be performed using Optical Coherence Tomography (OCT). These yield high resolution, useful images but it can be arduous and time-consuming for a human to manually label them. This presents a perfect opportunity to apply convolutional neural nets to segment the scans.

Enjoy a welcome meeting to the Math Monday series. Due to changes to campus policies, we will be hosting a virtual meeting with Carol Schumacher entitled "All Tangled Up." Join us at 3:10 p.m. to hear the presentation. You can join us by clicking this Zoom link.

Toys have inspired a lot of interesting mathematics. The Spirograph (TM) helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve “rolls” along another curve. Another children’s toy, the Tangle(TM), inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a “tangle curve,” which is made up of quarter circles.  The resulting roulettes we named “tangloids.” In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties.  

Plan to meet at the outside doors to Hayes Hall, near the parking lot at 3:10 p.m. The hike will be about one hour in length, but anyone who needs to return earlier is welcome to do so. Please be sure to bring something to drink.