Join the Mathematics and Statistics Department for a variety of stimulating math talks. We will meet every Monday from 3:10 to 4 p.m. (unless otherwise noted). For those who are on our distribution list, instructions on how to join each virtual meeting will be sent to your Kenyon email. If you would like to be added to the distribution list, please email Emily Teater at teater1@kenyon.edu.

## Upcoming Events

## Fall 2022

Welcome back to the Math & Stats Department! To celebrate and meet up with all of our math friends, we will be going on a nature walk. Come say hello to all your fellow math and stats students and faculty!

We will plan to meet in front of the doors to Hayes Hall at 3:10 p.m. A water station will be set up in front of the building, but you are encouraged to bring your own water bottles. We will be leaving in two teams for different nature routes. One will be a route on flatter paths and one will be on paths with more hills.

The Math and Stats Department is looking forward to seeing all of you back with us again for our Math Monday program! Join us for a little outdoor fun as a refreshing breather from classes. We hope to see you there!

You've probably heard that π is an irrational number: its decimal expansion never terminates and never repeats. But has anyone ever tried to convince you of this, or have you just been asked to accept it?

Bob Milnikel will help coordinate all of us working together on a proof of the irrationality of π. Individuals or teams will be given small algebra or calculus facts to establish, which we will then assemble into a proof that π must be irrational. No knowledge of mathematics beyond first-semester calculus will be needed.

Join us in Hayes 109 from 3:10 to 4:00 p.m. for this fun activity and presentation!

Meet and greet with your fellow math/stat students and the math and statistics faculty. Say hello to our math community and hear about all the exciting news in math and statistics. Learn about exciting opportunities and our Math Monday series.

Join us on Monday, Sept. 19, from 3:10 - 4 p.m. on the Peirce Hall patio. Free snacks, tea and lemonade will be served. We hope to see you there!

In this talk, we will discuss how to measure the "size" of fractal sets like the Menger Sponge (modeled by the cube with lots of holes in the hallway of the third floor of Hayes Hall). In particular, we will develop the notions of Hausdorff measure and Hausdorff dimension for sets in R^n. This talk will include lots of examples and pictures. Calculus students are particularly encouraged to attend.

Join us on Monday, September 26, from 3:10 to 4 p.m. in Hayes 109 for this presentation. We hope to see you then!

Come find out about the research done by some of your fellow students. In the first part of this series, we will feature students who did research off campus last summer.

Ethan Cripe Bonnell did research this summer at the University of Michigan-Dearborn. Ethan explored various group actions on sets of chords, particularly on unified sets of triads and seventh chords, and categorized these groups by their structure and cardinality relative to the sets upon which they act.

Saurav Pandey did research through the OSU SURE Program for the summer. The focus of the research was to optimize an algorithm written by Hittmeir that is able to find an element of large order at about the same cost as checking the order of a given element. For inputs N and delta, this element has an order of at least delta.

Finally, Ella Wilson did research at Yale’s REU SUMRY Program. Her research was to find the minimal splitting surface of the ideal octahedron in the Poincare ball using combinatorial methods.

Join us on Monday, October 3, from 3:10 to 4 p.m. in Hayes 109 to hear this exciting panel of presentations. We hope to see you then!

Find out about the research done by some of your fellow students. In the second part of this series, we will feature students who did research on campus over the summer.

Yiyang Lu worked with Noah Aydin for their research titled "Building a Workbench for Implementing and Testing Error-Correcting Codes." The project was to build a platform for testing error-correcting code schemes under a binary symmetric channel. The system allows experimentation by encoding data using a selected coding scheme, introducing errors, and then attempting to recover the original data by decoding the distorted data.

Fatma Mahmoud also worked with Aydin during the summer for a project titled "Search for New Linear Codes Through the BCH Bound and Its Generalizations." Fatma explored BCH codes in search of linear codes with better parameters over small finite fields than the best-known linear codes through the BCH bound and its generalizations. The goal of the project was to exhaustively search for new linear codes among BCH codes without having to do computationally expensive minimum distance calculations that take a very long time and might not even finish.

Vishad Onta worked with Aydin to work on the project "An Updated Database of Z4 Codes." This summer they searched for new codes over the integer ring Z4 among the classes of cyclic and quasi-cyclic codes by adapting the ASR search algorithm for finite fields. The search yielded thousands of new codes that have been added to the database of Z4 codes that we maintain. The database contained very few free codes. They increased this number significantly.

Kyle Kelley worked with Carol Schumacher on the project titled "All Tangled Up: Geometry of Tangloid Curves." They investigated properties of tangloids, piecewise curves created from rolling a small circle with a fixed pen around a series of circular arcs. These tangloid curves are composed of hypotrochoid and epitrochoid segments, and the resulting images/animations are fascinating.

Finally, Andrew Nguyen worked with Brad Hartlaub on the project "Power Study of Nanoparametric Tests for Interaction in Two-Way ANOVA." Tukey's test and the F-test are the known parametric tests for interaction, but may not be reliable when assumptions are violated. Can we develop new nonparametric tests that are more robust and more effective than existing tests?

Join us on Monday, October 10, from 3:10 to 4 p.m. in Hayes 109 to hear this exciting panel of presentations. We hope to see you there!

Visiting Assistant Professor Kitty Yang will be sharing a presentation on patterns out of chaos. We will play the Chaos Game to see how patterns can arise from "chaos." We will define Iterated Function Systems (IFS), and explore an important dynamical concept - the attracting set of an IFS. All students are welcome to attend, especially those who might be interested in taking the Special Topics course on Dynamical Systems in the spring semester.

Join us on Monday, October 17, from 3:10 to 4 p.m. in Hayes 109 for this exciting presentation. We hope to see you there!

Learn about the research done by some of your fellow students. In the final part of this series, we will feature a mix of students who did research on and off campus this summer.

Phillip Diamond worked this summer with Benjamin Schumacher of the Physics Department on his research titled "'No-Hiding’ Theorem in Modal Quantum Theory." Over the summer he researched “no-go theorems,” or statements of fundamental impossibilities in quantum physics, in a toy theory called Modal Quantum Theory. In particular, Phillip investigated the “no-hiding” theorem, which asserts the impossibility of perfect encryption of a quantum state. In the end, he discovered a surprising connection between irreducible quadratic equations and whether a state is "hide-able" or not!

Malcolm Gaynor worked with Zhu Wang of the University of South Carolina this summer for his research titled "Dimensionality Reduction in the Parameter Space (by the Active Subspace and Nonlinear Level Set Learning Techniques." The "Curse of Dimensionality" refers to the problem faced when modeling the output of functions with many parameters in a large dimension. When the dimension of a function increases, the computational costs associated with modeling this function's output increase exponentially. Thus, the active subspace method and the nonlinear level set learning technique will employ linear algebra and neural networks respectively to decrease this computational cost.

Finally, Jose Nino worked with the Federal Reserve Board of Governors for his research titled “Analysis of Nonfinancial Firms and Risk Appetite." At the Federal Reserve Board of Governors, Jose worked mainly with Christine Dobridge, senior economist in the Capital Markets section in the Research and Statistics division. Over the summer, he worked on analyzing nonfinancial firm dynamics in the economy by creating visualizations and summary statistics using R. He mainly worked on creating time series graphs showing how nonfinancial firms' perceived risk appetite has changed over time using a new leverage measure.

To hear more about these exciting research projects, join us on Monday, October 24, from 3:10 to 4 p.m. in Hayes 109. We hope to see you there!

If you rotate a geometrical shape by 2π radians (360 degrees) about any axis, you wind up with exactly the same shape, just as if you did no rotation at all. However, this simple fact — seemingly obvious — is actually not true for quantum particles with spin! We will explore the subtle difference that a 2π rotation makes — how there can be a difference at all and why that difference is one of the most important ideas in all of mathematical physics. (Though we will grapple with profound concepts of matter and geometry, this talk should be accessible to anyone who lives in three-dimensional space.)

Benjamin Schumacher, professor of physics at Kenyon, will be joining the math & stats team for the day to share this exciting presentation. Join us on Monday, October 31, from 3:10 to 4 p.m. in Hayes 109. We hope to see you there!

Semiconductors are ubiquitous throughout modern life, and sputtering targets are an early link in the chain of production for semiconductors. Throughout the creation process, statistical analysis is used to drive new development, limit waste, and ensure quality performance. This presentation will cover the basics of sputtering target creation and the role that mathematics and statistical analysis play in the manufacturing process, sharing a somewhat esoteric part of the process for those who may be interested in pursuing it in the future.

Michael Lewandowski, a quality assurance statistician at Tosoh SMD, Inc. will be visiting our campus to share this presentation on the manufacturing applications of statistics. Join us on Monday, November 7, from 3:10 to 4 p.m. in Hayes 109. We hope to see you then!

Daryl Swartzentruber, a Ph.D. candidate at the Ohio State University, will be visiting campus to share highlights from his graduate research. Causal inference methods allow researchers to estimate the treatment effects even in the presence of confounding variables. These methods include regression discontinuity (RD) designs, in which treatment assignment depends on whether the value of a running variable exceeds a cutoff. RD designs are increasingly popular in educational applications due to the prevalence of cutoff-based interventions. In such applications, sample sizes can be relatively small or there may be sparsity around the cutoff.

In this talk, Swartzentruber will present some of the contributions he has made in his dissertation research to small sample RD estimation. He will propose a new metric, density inclusive study size (DISS), that characterizes the size of an RD study better than overall sample size. He develops a bandwidth algorithm and variance estimation for a partial linear model estimator. He will apply these methods to simulated data and also analyze the effect of an intervention he implemented in an introductory statistics class he taught.

Join us on Monday, November 14, from 3:10 to 4 p.m. to hear about Swartzentruber's research. We will meet in Hayes 109. We hope to see you there!